Well no, the whole point is that there's shit on you in the first place already, not touching it is not an option.
You clean your arse with water so that it's clean and not just wiped with paper, just as you afterwards will wash your hands instead of just wiping them on a paper towel.
Well, that comes down to cultural or personal preference. Some cultures consider feet unclean. Some people consider the anus unclean. How clean you try to make a body part depends on how clean you consider or expect it to be.
You clean your arse with water so that it's clean and not just wiped with paper, just as you afterwards will wash your hands instead of just wiping them on a paper towel.