In hospitals you have sick or very sick people and people with open injuries. You can't take hospitals as the common scenario.

Interestingly this is actually a solved problem that we have forgotten the solution to. Copper naturally kills most pathogens. Brass door handles therefore act to prevent touch based spread of pathogens -- but plastic is cheaper.

Brass works fine too.

I do actually say use brass rather than copper in my OP for this exact reason.