It’s also a hygiene issue. Bathrooms are notoriously covered in fecal particles, one of the reason why flushing with the lid up is not a great idea. Having a door at least provides some protection against your bed also being covered in them.

Hotel beds are covered in far worse, a few more floating poo particles coming round the corner from the loo (after all, even if there is a door, it isn't always closed by prior guests, and they may get into bed without washing hands or worse) is the least of your worries.

Fungus still everywhere though.