360, and even xbox1, has a shitload of parental controls. you can ban games with M, T, etc. ratings or just keep all accounts from playing online. I'd know, my first Live account was made when I was under 18 and I didn't lie about my age, but for whatever reason I made an alt account (I think for japanese demos) and that was given parental controls and it was such a fucking hassle to try to undo restricting myself, and that was KNOWING the password. Obviously your kids aren't going to play anything you don't let them.
seriously though, you can easily enforce parental controls if you want to. it's like the most transparent UI ever.