None that I have been able to notice.
There is your answer. The play between the upper and lower doesn't matter. Changing the upper to another lower also does not change the POI.
The AR upper locks the barrel assembly, receiver and sights together in a constant relationship to one another. The reality is, the part of the AR we commonly call the "upper receiver" is analogous to the stock of a bolt action rifle. The actual receiver of an AR is the what we call the barrel extension. It's what the bolt locks into and holds the pressure of firing.
No stress at all is placed on the upper when it's dropped onto the lower. There is no contact between the lower and the barrel extension or the barrel. There is no contact with the bolt when the bolt is in battery. Because the lower simply floats on top the lower, because there are no fasteners that need to be torqued, the contact between the two halves is without any kind of force or stress to distort the upper.
The play between the upper and lower has no more affect on mechanical precision. (What we are talking about is actually precision, how close bullets group. Accuracy is how close we hit to the intended target.)
I'm moreso wondering how much the upper and lower movement affects POI in different shooting positions and if reducing the amount of play between the two can affect accuracy. It seams the group consensus of those that have actually tried it is that it makes little to no difference. I'm willing to accept that but I don't really like accepting something blindly without doing some testing of my own to confirm. I've disproved plenty of my own conceptions of what I believed to be fact through testing.
What many people don't realize is that when a loaded magazine is inserted in the well, the top cartridge pushes up on the lower and takes out the slop just as effectively as any polymer Wedgelok. The loaded mag also has the advantage of not hardening from time and chemicals to fall apart inside the action. Load up a magazine and test it for yourself.
Where this is all coming from is that I had a Savage BVSS that I rebarelled a few years ago with a criterion 223 barrel. I was never able to get the rifle to really wow me with accuracy. About .75 to 1 moa for 10 shots was the absolute best I could get out of it, though it would shoot nearly any load into that group size....After I glass bedded the action into the stock you could not move the action at all relative to the stock and it would then shoot .5 to .75 moa with any load and bullet.
Any rifle that consistently shoots
ten shot groups to MOA is awesome. Any rifle that consistently shoots ten shot MOA groups with any bullet is amazing. A rifle that consistently shoots ten shot groups to .75 MOA with any kind bullet after a simple bedding job is legendary!
The AR I'm working on now is in about the same just under 1 moa category with the right loads and bullets, though as of yet I have only tested a few load combinations. But if there is the potential to reduce that by even .1 moa then it will be a worthwhile and enjoyable exersize to see what I can do with the upper and lower fitment. Obviously an AR by design cannot place the upper and lower in tension to one another but I'm thinking of reaming the pin holes in the upper to press in a tight tollerance bushing in the front and epoxying one in the back to get the spacing perfect, and possibly working on some kind of standoff to eliminate as much side to side movement as possible. This is just the kind of stuff I like to mess around with.
Don't bother reaming the pin holes or trying to bed the upper to the lower. That stuff won't help. If you are serious about getting the best precision possible from your AR, start with a quality match barrel with a matched bolt. Mount it in either a forged VLTOR upper or the newest generation BCM forged upper. Both are designed to be stiffer than other uppers and offer a nice tight fit between the barrel extension and the upper. The next item is quality ammo, but you've already got that covered.