I’m surprised by this as 1.5 thou is probably less than the amount steel moves due to the temperature difference between winter and summer. If I made sure my planes were always flatter than that, I’d have much less time for planing, if I ever got to that level of accuracy to start with.
The last LN plane that I had was 1.5 thousandths hollow. I spent less than an hour correcting it to flat. A 14 or 15 inch long plane with a 1.5 thousandth hollow will be almost impossible to plane a match joint that closes unless you stand on the plane. You cannot use a plane properly to do that kind of work if it cannot cut flat or slightly hollow under it's own weight and no more than the downforce on the handle.
I hear this all the time "you can't work to that level", that's false. You can work as reasonably close as you can see in flatness, which is a small fraction of that.
I hear the same thing "a serious woodworker wouldn't have time for that". With all due respect, that's garbage. I could teach a mediocre woodworker how to flatten a plane to that spec from end to end in a matter of half an hour, both for convex and concave planes.
And, no, a plane that is 1.5 thousandths concave will never be flat or convex or 3 thousandths concave at any time no matter how much the temperature changes.
The other part of this is discretion - knowing when it matters (1.5 thousandths doesn't matter at all if the plane is convex and not twisted. On a long plane, two or three times that doesn't make an undesirable plane. And putting a plane between two boards and pushing on it with the toe and heel supported to see how much you can get it to move is a bogus test - I've heard that before, too. You don't plane with a plane sitting on two boards on the toe and heel.
I answer this kind of discussion a lot. I have a lot of experience flattening planes and being able to measure when they're actually flat, despite not being a professional and despite spending about 200 hours a year woodworking. Seeing assertions made out of lack of experience, or from machinists who don't use planes, or whatever else gets really annoying.
It misleads people. This is not a particularly high skill exercise. It's practical and can be accurate without being time consuming (though it's hard to get away from buying a straight edge that actually meets an accuracy spec, as well as a small set of accurate feelers to go with it.)
