Why the AR-15 can shoot as well as it does is a mystery.
If we look at the conventional receiver/bolt relationship in a bolt-action rifle, we see that the level of precision put into the tolerances and trueness of the action, bolt face, bolt lugs and lug recesses constitutes a majority of its performance potential. This precision then extends to the interaction of the stock with the action. Bedding has to be done using the right ideas and the lowest tolerance for imperfections, and barrel selection and fitting are also done in accordance. The rifle components become a unit, more or less. This rifle should conduct firing forces the same way on each shot. That's where the good groups come from.
But the lockup in the AR-15 is all in the bolt and barrel extension. The bolt locks into the extension, which has become a part of the barrel, and it's as if the bolt, cartridge and barrel are hanging in line, in space. Of course, everything else is still attached, but nothing else really has any positive influence. This is what makes it possible to put this upper on that lower and get the same results on the target. Every time. Compared to the "unitized" precision bolt gun, an AR-15 is intentionally disjointed.
The bolt carrier has a lot of play inside the upper receiver. That's not a bad thing. This play is necessary for the rifle to shoot well and function reliably. Efforts have been made to snug the fit of bolt carriers into uppers. Functional maladies, however, buried most oversize-carrier ideas.
Anyone who's handled many AR-15s knows they rattle. This comes from the upper and lower receiver fit, and is in the front pivot and rear takedown-pin contact areas. This is disconcerting since benchrest rifles don't rattle. But it's binding, not looseness, that's detrimental to accuracy.