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In terms of environments for things that create odors, I would think a rinsed and air-dried brush would be less likely to promote odors than one left to dry with soap in it.

I've never washed a brush in 30 years. I rinse them, shake the residual water out of them, and then I hang them bristles down to dry. I've never noticed any untoward odor coming from them.

I doubt that dead skin cells are capable of much in the way of multiplication. They can't even divide.

I've been very quickly snapping mine to get the water out. It's lasted 30 years now.