Besides being gross you are not going to get athlete's face or anything.
For safety I've asked a few to clip their toenails but no way I'm going to ask someone not to sweat - that's what I want them to do. I am more worries about slips and falls because of wet spots than the bacteria.
By the by - the bacteria on human skin, the type you would most likely find in sweat, is part of a natural symbiotic function. Believe it or not those critters keep us clean and smelling a lot better than if they were not there.
Problems when they occur are most likely when a few pathogenic bacteria have a chance to grow and multiply outside the dojo. Athlete's foot (feet?) don't beget athlete's foot until after they've had a chance to stew in your socks for a bit.
So boys and girls, shower after training, dry your toes well and change your socks. A little bit of powder if your worried.
Good dojo practice is a to sweep the dust and run a damp (clean) mop every now and then, common sense.