I'll try and keep this short and simple.
I would rather not re-create the whole diatribe on small arms primers, but I will state that there is more than one primer design type.
If we split the discussion between the type where the anvil feet are flush with the cup, say like a BR-2 or BR-4 version, and contrast it to something like a CCI-450 where the feet are proud of the cup, those are the two sets of issues for a simplified installation discussion.
With a flush cup, you just get the cup to the bottom of the pocket and Bob's your Uncle. Done and over, not complicated.
Trouble comes when the cup is left short of the bottom. This issue is simpler because the "crush" or "consolidation" is built into the design and all you have to do is get it to bottom.
And then there is the second kind where the burden is on the reloader because the feet sit proud and are not meant to be driven flush with the cup.
When the anvil feet sit proud of the cup, the responsibility for "crush" is up to the user. The dimensions are not such that they are intended to be crushed to get the feet flush. The ideal values are on the order of 0.002" - 0.006" for typical ones, so say on average you are targeting 0.004" +/- 0.002" crush or reconsolidation. (Some other brands used to run 0.002" - 0.004")
When I used to specifically test primers on a test stand, you would all agree with the manufacturer's recommendations for seating, and the door opens for trouble when you are outside of their intended range.
When I have tested my own ammo it does show an effect on target, and on the chrono, but we would all probably agree the "good window" shouldn't be too difficult to hit if you are paying attention to your brass inspection.
My own pet peeve is that they do not publish these dimensions or recommendations to the consumer right on the packages. It would end a lot of arguments but once again I am left shaking my head. There really isn't much direct information in the public domain, and that is a shame. YMMV