The problem with the 5.56 armor piercing is it only works to about 100 yards. The standard bullet is 55 grains and the armor piercing with a tungsten rod is over 100. It’s just too light a round.
I believe the problem with the .308 is it requires a larger boldface, so you are carrying a medium action like the M10 that soldiers love to hate, and the much larger casing diameter limits you to 20 round mags.
The 6 Max uses the same, small rifle action and boldface as the 5.56, but with a larger, untapered case. It fits 35 grains bang powder instead of 29, which is a significant step up, and shoots bullets from 90-104 grains. So you have more energy but not so much that you get stiff recoil and heavier rifles and ammo.
The Sig XM-7 and Fury ammo requires a medium bolt face and action, and its larger diameter gives you 20 round mags. Soldiers hate it.
The .308 is a great round, but .24 (6 Max) ballistics are far, far better down range, and they recoil much less.