I'm sure there are zillions more mouth germs on it than floor germs.

I run all our toothbrushes through the dishwasher once a month and after anyone's sick (as well as clean and lysol the toothbrush holder). Checked with dentist who said this was fine. I replace them when they're worn down or every six months or so. Toss it if you want, but IMO it's not necessary. The dishwasher will do.