It's been interesting to watch this discussion to see how the points have been advanced. It's always fun to watch master Jacob relentlessly pursuing a point of view.
I don't own a scrub plane, and mostly flatten boards and straighten edges on a planer. But every now and then I've had to resort to hand planes to do the job, e.g., a board too wide for the surface planer (jointer for David) that has to be used in that width. For the most part, as described by David, I just went at it with either my no 5 jack plane or with my no 7 try plane, both Records. It took some work, but I got there.
Then, many years ago I was inspired to modify a not very satisfactory Record no 4 smoothing plane - I had plenty of alternative smoothing planes kicking around, five including this one. I opened up the mouth with a file, and put a fairly hefty arc on the blade's cutting edge, and set the cap iron back so that its corners only just touched the limits of the arc at either side of the blade. In use, when the centre of the blade protruded by about 1 - 1.5 mm below the sole, only about 1/2 - 2/3 of the blade was exposed. It works reasonably well and in the past I've hauled it out sparingly to knock off the worst of the high spots in a board, or some particularly skanky bits of board face or edge prior to reverting back to the no 5 or no 7.
Then, one day many years ago (maybe twenty, I faced the task of flattening something long, wide, cupped and twisted again, and thought, "Screw this for a game of soldiers." So, out came my DeWalt hand held power planer, which took about ten minutes to do pretty much the same thing my home made no 4 'scrub' plane would have achieved in maybe half to three quarters of an hour.
I don't think I've used my modified no 4 'scrub' plane since, and it sits rather forlornly and perhaps a bit unloved in my toolbox. So, in conclusion, I'd say a proper scrub plane, much like my home made version, would probably end up mostly sitting in my toolbox primarily as some sort of decorative and slightly interesting artefact, especially as a hand held power planer is also to hand. Maybe I should offer up my lovingly modified hack of a no 4 scrub plane to the denizens of eBay. You never know, I might get £100 or more for it, it being a one-off and quite rare, ha, ha. Slainte.