For sure, peace of mind is priceless. And I'm not saying it can't make people sick, but it obviously doesn't make people sick at any non-negligible rates, or we'd be seeing those patterns. And I realize this isn't an actual issue for your situation, but closing the lid does nothing.

Public bathrooms have antimicrobial surfaces because people can't be trusted to wash the actual-disease-causing amounts of feces off of their hands. Healthcare settings obviously need to take every possible vector more seriously, and even they can't stop it without a sealed lid, which again, I've never seen anywhere. Like, there are bathroom attendants, people whose whole job is to sit in the bathroom all day, the patterns would be unavoidable and undeniable.