How does this have anything to do with 'public health'?

And almost any regulation gives a (relative) advantage to the people who can afford the lawyers and bureaucrats to furnish the documentation to show that they are in compliance.

Fecal particles are well documented as a vector for disease transmission, particularly an issue when travelling with someone who is sick but also just from the long term distribution of them into the room.

Going from no regulation to one does carry some of what you suggest, but there are already regulations about tons of things here (fire alarms, exits, building codes, etc) adding one more does not increase the need for lawyers and documentation.

The absence of a door strikes some people's sensibilities as mingling the capital-C Clean with the capital-U Unclean.

Which, as I think you're hinting, is largely distinct from anybody's actual health