Brakes are loud. They redirect gas to the sides, where there may be other shooters. The blast off a brake is sharper than with a plain muzzle or a flash hider and tends to annoy people. Brakes also increase flash signature if it's twilight or dark.
Brakes interfere with the gas coming off the muzzle. This may cause a decrease in accuracy compared to a plain muzzle or symmetric flash hider. The redirected gas can also raise more dust when shooting prone.
Generally 5.56 rifles just don't have enough recoil to make brakes worthwhile, in my opinion. The only brake I own is the one on my AK, and while is does reduce recoil and muzzle flip, it has the disadvantages I mentioned above.
The whole break/brake thing is kinda like calling magazines clips: it's technically incorrect and can lead to confusion. Muzzle break can be inferred to mean a broken muzzle. A muzzle brake can only be a device that reduces recoil and/or climb.
BSW