Recoil on the 308 is not that heavy unless you are recoil sensitive
Its not just about recoil. Its about muzzle control. The brake cuts down on muzzle jump, allowing you to easier spot hits, and helps with follow through and quick follow up shots.
I doubt any of us complain that the 22 rim fire has too much recoil, but a lot of people improve their rimfire shooting by adding a brake to their 22 rifles and pistols.
I have a buddy who put a brake on his rather heavy 223 varmit rifle. It holds the muzzle down so you could see the impact when you hit PDs.