Fire, man. Just let the fire clean it. Never saw the point of wire brushes unless you're leaving food on the grill when you're done with it.

I think a lot of people don’t let their grill get hot enough. I know I have problems with cleaning my smoker racks (and my wife won’t let me run them through the dish washer) so I have to throw them on my charcoal grill when I’m heating it up.

Yeah, probably. Charred food is not good for you really, but it's going to be on there anyway after you cook on a grill no matter what (unless it's like, a George Foreman...?). I can't imagine the bit of carbon on the grill from the last session would ever cause more harm than normal charcoal!

Hot concentrated sodium hydroxide will do it. Or oven cleaner, if you can't get chemicals. It won't damage steel, but will dissolve aluminum. Ammonia works too, but not as effectively.

OxiClean (or other clean-in-place products) should do a good job if you have a way of submerging the grill top. Brewers use this to clean fermenters and other equipment.

If you could get the grill to heat over 700°C, organic gunk would gasify.

Would it be safe/feasible to use a butane or propane torch for that? Would there be an issue of carcinogenic residue? If not, then a handheld torch is cheap and easy to use, and goes well last 700 degrees.

Haven't tried, but I bet vinegar would wipe it down pretty well.

Wiping with vinegar will cause rust. You want to go the other way - alkalis will convert grease into soluble compounds without damaging the steel.

So say something like a solution of baking soda and water?

Yes, but it'd be very slow. Lye would be much more effective. But any solution strong enough to saponify the grease will be strong enough to damage your skin, so use gloves.

I usually just burn it off.