Everyone sucks here
Nobody finds your ratty little poop machines cute but you and NOBODY wants to play hopscotch trying to avoid the mess you have left using public walkways as a toilet.
That said, don't buy land with a public easement and then try to control public use of it. It doesn't matter how many billions you have - you don't get to keep a public trail to yourself. If you want seclusion and privacy, buy some land without an easement through it.
This is no different than people trying to kick someone off the sidewalk in front of their house/business. You don't have the right.