Imo, the porcelain throne is a place for quiet reflection...
Hence the statue:
Very easy to reflect quietly when no one is there, so door stays open
If people are there, then obviously it's more difficult, lol Seriously though, doors are to keep people out when you don't want them there, so if there's no people there's no reason to close the door, so I keep it open.
Like others with pets, my cat always likes to follow me to the washroom for some inexplicable reason...particularly awkward when she comes and sits right by my feet, at which point I give her the "are you serious?" look and she continues to purr contentedly
She could be off sleeping in my closet having nothing to do with me, but the minute I go to the washroom she comes running as though it's the event of the day lol