Mixed views and picking up steam! : )
We risk tending towards the sort of reaction which seems often to arise on woodworking forums when talking the use of engineering (more correctly in this case 'fitting') methods and tolerances on tools : )
There are not too many absolutes or black and white answers in this territory. It's a matter of degree, of expectations, of perception, of technique (in both set up and use) and of what you are used to.
If a plane is working for you it's fine.
If a method works for you it's fine too.
It's daft to come up with a solution and only then to seek a problem to apply it to.
It's often possible given enough time and experience to develop technique which as before can up to a point (beyond which may not matter to the individual concerned) work around some problems in a hand plane. It is however only one solution....
An analogy from real life industry. A skilled operator finds ways to tweak e.g. a complex injection moulding machine into working with a specific mould when others can't make it perform. He gains a reputation as a magician, and for years leverages this to his advantage - lording it over all.
Yet there is no magic, only the need to gain an understanding as to which parameters must be controlled to which settings for the process to work reliably - modifying the equipment if necessary to gain this control. e.g. by making sure that the mould cooling water temperature is accurately controlled, the mould is pre-heated to a certain temperature before use etc.
Once done and the methodology standardised the magic evaporates and the machine performs reliably for all.
While it may not matter to everybody, and isn't in lots of cases necessary what is clear is that precision makes a big difference to how consistently both hand and power planes work.
As D-W: 'Two things where flatness shows up on an already flat board or edge. Match planing/edge jointing, and smoothing a surface from end to end moving right to left or left to right. if The plane in question can't do both of those, then something is wrong.'
This last is a fundamental point. If the piece is not flat then an out of flat sole will catch the high points but not in a very predictable manner. If the piece is flat then an out of flat sole (depending on what the problem is) may/may not cut, and if/when it does it will probably take the surface out of flat.
Precision in wider plane set up (for fine work) is a bit like precision in sharpening.
As pointed out above by TTrees (?) a really sharp and and accurately formed cutting edge (which many especially years ago would have regarded as overkill) will sail through difficult material where one less so will cause tearout and so on. The latter giving rise to perhaps a mythology about doing this and this to prevent tear out, needing to use a scraper or whatever
I've been through this on a 410 planer thicknesser by a well known Austrian company. A hump from the factory (likely caused by poor fixturing during machining, and predictably enough inside their self awarded 'permitted' tolerance/not covered by the warranty) of several thou in the wrong location on both tables required drooping of the infeed table to partly compensate and made planing a straight board a lottery.
Once the tables were made truly flat (the how is for another thread) the magic as above evaporated - it now joints straight everytime, the tables are in the same plane and it responds predictably and identically to fine adjustments across the full width of the tables.
Many have a hand plane that just works well, but don't know why - but that may not generally be the case for all examples of that tool. There may even be many defects that don't matter a lot in the good plane.
If on the other hand you have one with problems they can often be fixed.
Not only that but some extra precision can make quite a difference. Back to our 0.001in shaving from a smoother again - can one be expected to perform reliably in this case unless the sole is flat in the right places to within a lot better than 1 thou?
The point is that given the right technique it often doesn't require much extra to go a bit further to achieve precision.
If a plane is way off then the linked video shows the sort of steps required to sort it out - presuming that's possible to do so by removing metal. Going at a Lie Nielsen could however easily leave it worse than it was if the right methods are not used - I'm not convinced about the use of sandpaper shown in the video. If it had real problems should it perhaps instead gone back to the factory? Precision is a large part of why the premium pricing makes sense...
That said I suspect that some of the cost of a Lie Nielsen or a Veritas is to carry the cost of the many specialist but likely low volume planes in their ranges too.
Wet and dry on flat surface will go a long way towards flattening a sole - that was how I after some careful file work years ago first flattened the way out of whack No. 5 Clifton. (it sucks down nicely to resist puckering when wet and probably is of consistent thickness) It's since had a second and finer flattening on a surface plate.
A true straight edge with a feeler gauge and/or a light tells a lot too, but bear in mind that the finest feeler gauge normally offered in sets is 0.0015in ( 1 1/2 thou) thick - which is more than the thickness of a fine shaving off a smoother = a smoother sole needs to be quite a bit flatter than that)
A Starret straight edge (it's hard to work without a reliable straight edge of some sort) will meanwhile cost very close to the price of a small granite surface plate. The latter meanwhile works in 2D - it picks up twist as well, and used with blue permits getting down to much finer tolerances than with the usual woodworking methods if required.
More to the point - working off a surface plate is no more labour intensive than any other method, and the kit is not a big investment viewed in the longer term. It's just not common practice in the woodworking world...
This is beyond the scope of this thread, but I'll answer two of these - by the way, i'm assuming if you have a flat panel to test a plane against, you can prove it's flat by checking its length and diagonals with a straight edge. You'll find with a little bit of experience you have some bias. I plane things a little hollow through their length because the bias is always for some % of imperfection at the start - not much. if I get a plane that planes the ends off of things after that for a while, it's an instant indicator.
If you manage to make an ideal sole (not encouraging chasing this), you will see little to no light on the edge of a starrett straight edge almost to the tips of the plane and just a bit at the tips. No matter where you put the straight edge. A 1.5 thousandth feeler won't come close. How easy one fits under a straight edge is an indicator of how far off you may be and where. if it's in the last inch at the to and heel, then it doesn't matter. It's probably preferable.
These numbers are kind of meaningless if something isn't put to them in terms of use. If you see 2 thousandths hollow, you will have use problems. If you see 2 thousandths convex, you won't. if you see a hundredth convex, you will for jointing or smoothing - it's not a critical issue, but it's annoying.
I have two surface plates. if you stay with this and it's toolmaking related, you'll come around to my point of view. A long lap of glass is a maker's tool. it will help you with fitting and truing things, but it's also useful for making. An 18" surface plate is often too short for what you want to do, and far too heavy for regular moving around and casual use. by that I mean physically annoying, not impossible (i righted my bench - 350 or so pounds before vises - alone after attaching the legs. I find the surface plates annoying and at this point now making tools, sometimes to very high accuracy within the premium plane specs easily, there's no real use for them). the cost of entry with a float glass shelf 3-4 feet long is that you need to be able to plane a flat and stable surface to go under it, and that surface cannot have grit or anything on it when using the plate, but it is monstrously useful and easy to use.
Comparing the 24 inch starrett then to a surface plate, it gives you an independent check that's far more useful. You can use it walking around, you can check matched edges with it, you can use it to mark with a knife or pencil, or hold down leather and cut it cleanly.
My bogey on a jointer is an hour with a file or a smaller block and the long lap. The goal of the plane is to plane a through shaving on an edge indefinitely and leave a match fittable joint without much tension.
The fellow who got me into woodworking is a mechanical engineer. he views things like we're discussing from the lens of hiring machine shops in his day job, and the things they do. It's not really a very good background for woodworking tools, because the work to flatten or the fixes to deal with tool problems are often far more appropriately dealt with by coarse work then finishing with a bias to ensure fit. They aren't like two flat surfaces that hold each other together with a vacuum - there's no scraping and flaking or things like that. It doesn't take that to get a plane that will shave a continuous shaving length and width-wise that will be limited by practical sharpness constrained by the hardness of an iron.
I puzzle about coming up with advice that will be good for someone other than "send the tools to me and they will come back working well". That's an idealistic thought, but you end up getting a lot of tools from people that don't work well, and if you check in with them a year later, you find they haven't used them. it makes them feel good to have something working well, and maybe they tested and confirmed it and were ecstatic. But that's not my objective.
A more practical thing for someone who doesn't know much is to learn to do basic sharpening of a plane iron, clean up the front of the cap iron and buy five of each, keep the best, sell the other four. In the end, it will cost, for example, what two vintage planes cost. For a jack plane, this isn't necessary, which leaves it being the way to go for a smoother and jointer. probably 2 of 10 jointers that I've bought would fit in LN's spec. I've bought more than 10, but guessing at that. I have two right now that were ever so slightly low at the toe and heel but would've passed LN's spec test. Some others, much further out. I think that's an OK strategy, but it fails from the viewpoint of many not being comfortable selling things on ebay. Friend who got me into woodworking has plenty of tools that he doesn't care for, but has never sold anything. It's a daunting idea to him.
if we talk about standardized methods and uniform usefulness for all, we'll be into jointers not taking an hour and a lot of wasted time. Becoming a craftsman in general has a lot to do with discretion, and this is a good time to start learning it. When standardized methods are used for something we purchase with an attempt to a very fine spec in everything measurable, we end up paying a lot for things we don't need.
LN and LV no doubt have much longer production routines than stanley did. It ensures consistency, but it doesn't add value for an experienced user. It adds value for a beginner, but even then, mostly perceived value. The perception of safety. it can be so reassuring ("the only way to get ___ and be sure it will be OK") that it leaves people with the idea that they cannot be involved in ensuring they have good tools, or that they can't be without a process that fixes 10 things every time when on average, 2 need to be addressed. that's too limiting.
I don't know how far along you are with precise sharpening, but that is generally a matter of experience and good grinding. the actual honing of an edge was never a sloppy thing until probably after 1900. the older texts address everything from prep for final edge treatment to final edge treatment, and they refer to things like turkish oilstones, which are capable of a better edge than something like an 8k waterstone. Like getting tools in shape, it's easy to get fascinated with the precision and lose track of how to get it quickly in a way that matters and may not be what is expected conceptually. especially if you get sidetracked in discussions about shapes of bevels, etc aside from not having the bevels encourage errant work honing (like a convex bevel will do).
Exploring more than just the precision is the key to getting it on things that aren't easy to set up (for example, if you can sharpen a chisel in a guide and do everything just so, what do you do when you get to a turning skew or an incannel gouge).