I've never understood the usefulness(from a military perspective) of a muzzle break. I mean a 3 foot muzzle flash will draw just as much fire as a 10 foot muzzle flash; Right?
I think you've got your devices confused. A muzzle break or "compensator" is meant to reduce recoil, sound tends to be increased. And reducing recoil can be VERY useful as you can imagine, especially with big recoiling cartridges like the .50 BMG.
A FLASH SUPRESSOR is what reduces that visible flash you are talking about. Also they seem to be more effective than you imply but still less effective than a sound suppressor which eliminates muzzle flash and reduces muzzle report significantly, while also reducing recoil. I also believe one of the reasons for having flash suppressors on military weapons is to protect the crown from damage, which it does quite well.