You're conflating who needs to take care of that - if someone on public land doesn't stay on public land, when they are out they can be charged.

I don't see why you need to change the narrative to be "OH WOE IS ME, THEY TOUCHED THINE PUBLIC, but pissed on thine private a bit". That can be charged with evidence.

People MAYBE doing a crime is not a crime, and is a fucked up premise for you to persue, I'm disappointed in you.

I hate to break it to you - the govt can define walking paths and public lines.