It's not that, think of the patients with wounds, or who are immune compromised from say, chemo.
Hospitals are notorious for passing infections from one patient to another. Lots of safeguards are in place, but handwashing is critical, and often overlooked. Gloves are meaningless without it, as I illustrated above.
Fitz, the mop water contains a disinfectant. A STRONG one.
Yes --- if they mix it right or change it when they should --- but how carefully are things like that always checked? I've seen some filthy hospital floors --- blood from a previous patient on the floor. I was shocked at a bathroom near an Emergency Room with used dirty toilet paper thrown on the floor piled up in each stall. It was obviously used by some pretty disgusting people --- more than one --- and hadn't been cleaned for hours.