This covers three strong aspects of Japanese culture - bowing, cleaning up after others and saying "welcome".
Do you know what's great about the way Japanese greet one another? You don't have to touch anybody. If that sounds squeamish to a paranoid extent, go back and read my post here. I've seen enough public peeing, nasal excavation, and women walking out of toilets without washing their hands to make me think twice about shaking hands in greeting. If you see enough unhygienic and disgusting behavior, you really don't want to be touching people the first time you meet them.
I'll miss bowing, because I don't know where people have been or how clean their hands are and experience has taught me to err on the side of caution.