Yes, and you totally stole it! Kidding.

I'm just glad others are agreeing with it. It'd be so easy to then start a new game and not have to worry about leechers or low-levels (low-lifes, haha) joining. This could easily show in the game selection list too, though unlike your suggestion, I think if a game has a minimum join level that is above your current level, the level number currently in place would display in red. If you still try to join it you'd get a notice saying you can't.