Here's an idea:
The sinks should be outside the bathroom.
That way, you can wash your hands after touching the dirty door, and everyone in the hallway can see if you don't wash your hands.
Are the doors even necessary? Just put a sharp left turn tiny hallway for privacy, blocks out everything but sound - most public bathrooms have them already
The sound is the worst part, I wish the bathroom in my office had music or something so I don't have to hear every detail of whomever is disemboweling themselves in the next stall over.
But then I'd rather have my highschool toilets which had a direct outside access. They weren't heated and thus were cold in winter but the smell was indeed ok.
I still don't want to touch a handle where it's guaranteed that people who just took a shit without washing their hands have touched, even if I'm about to wash my hands right after.
We should just all use those foot handles. Solves pretty much everything, but why are they so rare?
That...makes sense to me. Not only would you need one set of sinks, you wouldn't need to go into the shit and piss room if you just want to wash your hands.