Is the military really going to worry about the increased noise emitted by a brake on the battlefield, when any number of people are banging away, some/all on burst/FA? How about the noise from tanks, vehicles, bombs, mortar rounds , grenades, planes, ad nauseam?
Doubt the difference is noticeable after the first few seconds of battle. One's ears would "clamp down" and auditory exclusion would be the name of the game.
I strongly suspect that the military spurns brakes because they would MUCH rather have flash-suppression what with all the NVDs being used, and the penchant for operating at night (force multiplier). A muzzle brake would:
(1) Quickly ruin the shooter's night vision. (I know, it's not gonna last long anyway, but why rush night blindness if you don't have to?)
(2) Damage or render temporarily useless NVDs upon which we now rely heavily. (And not necessarily just your own, either...)
(3) Make a much better target for opposing forces than a flash suppressor.
As far as Tac rifle matches go, not everything they develop is a good idea in combat. Think fragile "space gun".