-You are overestimating the amount of shit produced in one siting XD. Also, I you get yourself dirty is YOUR shame, so more interest in keeping yourself clean. -You don't have to go that deep. Also, using a stick to clean your ass is very uncomfortable, one should expect that the romans would have found a better way in all its story.
P.S. I love being able to discus how people in ancient times wiped them selves.
-What should people care if one guy has a scratchy ass? Remember, in Roman time there was no concept of bacteria. -If there were so depth and small, maybe a stick will come in handy, don't you think?
Makes much more sense that the use it like we do nowadays with toilet brushes. Especially if there was a mural telling people to use it. Usually you don't have to reminder or care to tell people to wipe their own ass.
Sorry to be that guy, but it seems the romans didn't wipe with an sponge on a stick.
From a mural in the baths form the Secen Sages in Ostia Antica, it seems it was use to clean the toilets after use.
Absolutely anything you want (within reason!).