We only had huge messes on the floor a handfull of times, luckily, but when we did I would pick up any large items, but then otherwise tipped extra. There's no way I am putting my hands on a dirty restaurant floor and cleaning with a napkin. It might be nicer, but who knows what is on the floor and the last time it was cleaned. In Chef Mickey's once, a 2yo had a potty accident at the next table and poop literally fell on the floor. The mom did clean it up, but it wasn't sanitized or anything before the next family sat down, so had that been me, and I were on my hands and knees cleaning up my kid's spilled chicken nuggets, I would have had all that bacteria on me and never known it.
So I'll leave it to the waitstaff who have gloves, a broom/mop, bleach or lysol, etc.