I always go high heat on startup to not only get the grate really hot but to get a good bed of mesquite sticks going on the grate surface itself. (gas or charcoal, I do the same).
Once the grate is hot I use a heavy duty wire brush to clean it. I went through about a hundred wire brushes because I foolishly bought "bbq" brushes for years. Now I use the industrial metal brushes at ace. The ones that come on a wooden block and have a threaded angled insert on the back. you screw a broom handle like attachment with matching thread into it and cut it down to size.
My propane grill is a weber clamshell with thick heavy duty cast iron grates, my charcoal grill is a bastardized chargrill that got converted to charcoal after it's life as a propane grill died and now has stainless steel grates.
Any problems clean right up with the heat and a good metal brush. sometimes I'll spill in some beer or water on the cast iron ones to steam them up if something is troublesome.
Show me the bacteria that lives through 400+ degree temp and we can talk about the germ hygiene issue with my process.
I never use oil or pam or the like on any grill surface. Then again, I grill at least twice a week so rust is out of the picture.