Why can't those things exist like that? I mean, if someone can forge great ebony armor, why can't they slap together a bathtub?
Sarcasm?
Just to be on the safe side, forging an armor and a bathtub, sink or w/e is a little different. Just a little
Because bathtubs and sinks and w/e would require a complicated pipe system and some sort of powerful pump and a water tower. Do you really think that fits in TES's setting? Come on.
It's kinda like saying guns would be in Skyrim.
Besides, TES has a medieval theme, partly. People never took baths (or very very very rarely) during such times. So having a bathtub which you fill with water from a bucket wouldn't really work then either. And it wouldn't be connected to a sewer system then. So... again. No.