I find it's pretty hard to say that at a certain age a child is required to be independent, as it really depends on when they start potty training and become consistent with it. I currently have a two year old in my care who is completely independent whereas I'm still having to check and sometimes assist my 4 year old. They are just completely different kids who became ready at different times. But either way, except for in the very beginning, I too never stay with them the whole time. I might check in on them to make sure everything is ok. But otherwise I instruct them to call me once done to either help them wipe up or to inspect them. I guess I've been pretty lucky in that I've never had to deal with poop everywhere.