toilet

I'm careful enough to never actually touch any shit, so I don't need to wash my hands.

You probably don't know this, but there are still some "people" in the civilized world who take balls of tissue and shove them up their ass with bare hands immediately after shitting. Before everybody started using bidets, this was the norm and thus hand-washing was required for hygiene. Unfortunately, the few who still "wipe," while small in numbers, are big in germs, so hand-washing remains a social norm in many places.