...why should people have to clean up cat crap and cat piss from someone else's cat?

Because it's there. Like cleaning up- after pigeons. Part of the rich tapestry of life.   

And the same goes for cats killing birds or mice etc.

And for the evident variation between the USA and other countries when it comes to keeping cats confined to the house.

Our deaf cat right now is sitting by the glass waiting to go out for a brief walk round the garden to sniff the foliage. She's got no problem in letting us know what she wants.