If the "open" button both unlocks and opens, what use case is there for closing the door from the inside without locking it?

The doors take so long to close that it would be easy to press the button and immediately exit the toilet, leaving it locked but with nobody inside, effectively taking it out of use for other passengers.

I think it is to prevent vandals from closing and locking the door from the outside.

I use that button to close the door when I have finished using the train toilet. You have to race the automatic door and rush out before it closes on you.

(Of course the button should be outside).

Why do you want to close the door if you're not inside? If that's not the norm, doesn't it just indicate to others that the toilet is occupied?

Because they stink, and it's very unpleasant for people in the carriage sitting near the toilet if the door is open.