As mentioned, muzzle brakes ARE NOT a controlled accessory, there are no hoops to go through to buy, install or use.
As too their usefulness and do they work. I have a few and I'd say yes, they are useful and they do work.
I started out putting one on my 300 WM 1000 yard rifle. It reduces the recoil quite a bit, allowing my to enjoy my shooting a lot more. Also, and more important they reduce muzzle whip allowing for faster follow up shoots and allow you to better observe your hits or misses at distance.
After the results I put one on my 375 H&H, which makes it a pleasure to shoot. I have a mold where I can shoot jacketed/cast bullets meaning I can shoot my 375 fairly cheap, only paying for primers and powder. I can shoot more, get more practice which makes me shoot it better. Without the brake my shooting would be limited because I'm a wimp when it comes to recoil.
I shoot for fun, not to bet beat up by my rifles, and again, quick follow up shots. Kind of handy after spending hard funds for an elk hunt. It could mean a down elk or following an blood trail all night.
I'm putting one on a light weight 308 I built for my grandson, meaning he can use hunting loads instead of light Trail Boss loads, he can learn to shoot instead of learning to flinch.
Yeah they make noise, more so then without, but I don't shoot, and wont let any one else shoot on my range without proper ear protection.
Also I don't shoot on a crowded range so I don't disturb anyone else.
Before one condemns brakes, I'd like to see them try them.
If anyone is close to Newcastle Wyoming, give me a shout, I'll take you to the range and you can shoot my rifles with and without a brake and see for yourself.
This isn't an advertisement for muzzle brakes, I don't sell them, I don't make them and I don't install them on anyone's rifle but my own.
I just want my fellow shooters to enjoy their shooting more, and I believe brakes will allow that.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071