Not sure if you've been to Japan but they have some of the cleanest public facilities I've seen in spite of all the traffic. I'm sure people are coming through multiple times a day to wipe down all fomites.
New word to me and I have a pretty good vocab, so
If you touch the soap and the tap, that will surely transfer germs to your hands that the person before you left there?
Soap and water definitely work to reduce infections, even when using a shared sink. Look up what happened in the 19th century when people finally figured this out and started hand washing regularly, infectious disease transmission in settings like hospitals dropped dramatically.