Most of the cooked food is at least 100C for a while. Dishes and utensils in commercial establishments (at least in the US) are by law sanitized either with temperature or bleach solutions. (The silverware drawer is another matter.)

It's pretty hard for bacteria to live on a 200C grill. "Unclean" and "harboring live bacteria" are different things.

You'd be surprised how much care is paid to hygiene in commercial kitchens. It's quite different than cooking at home, as the stakes are a lot higher.