More accurate? Maybe so.
But you gonna reach out and touch some terrorists with .22 caliber? I know it can be done, and is often done, but for long range and sniping, given a choice, you gonna choose a .22?
M-16 @ 5.56 was originally selected for carry-that-much-more-ammo spray-and-pray, with a wounded Sovietski actually costing Ivan more than a dead troop. Center mass, full auto, 3-5 round burst, and then on to the next target. Sequential buckshot. Hayna or no?
The AR/M16/M4 can use a wide variety of calibers. If the .223 is your objection, lobby for them to use a better caliber. Why replace the platform?