Another way in which an AR is mechanically less inclined to precision accuracy than a bolt gun is the firing mechanism. The lock time of an AR15 is around 10-12 ms vs 1.5 to 2 ms on a Tikka and maybe 3ms on a Rem 700. Lock time is how long it takes between when you break the trigger and the pin hits the primer, during which time any minute movement of the gun will impact POI.
So you have a longer lock time, but that is further compounded by the fact that an AR15 also has about twice the mass in motion during that 10-12 ms, and that mass is not moving in a straight line with the bore the way it does on a bolt gun, in fact that mass (the hammer) is spinning round the hammer pin with quite a bit of force due to the spring tension.
So basically, you have a long time (relatively) in which your gun can get a hair off target, you (probably) have a trigger with a fair bit of over-travel, and you have forces in play inside the gun that aren't pushing in a straight line with the bore. None of that is conducive to being competitive with a bolt gun.
As with headspace and such, these are again things that can be improved in the pursuit of accuracy - a number or AR15 trigger systems feature a lower mass hammer and significantly improved lock times, but again, going there, moves us away from the type of robustly reliable trigger system that the mil-spec assembly is, which you can drag through the deserts of Afghanistan bouncing around in a humvee and still expect to work flawlessly when the locals start shooting at you and you want to shoot back.
And again, this is not a reason to not buy an AR15, this is a reason to buy a variety of AR15s!!

