I've gotten so used to dropping my clothes before bathing I forgot this was even a minor issue I used to have.
I only ever had one problem with dropping my clothes and it was when Oriana picked up my shirt when she RPed getting clothed after a steamy bath session. I had to RP that I lost my shirt and ask her if she's seen it to get it back. It was enchanted so I kind of wanted that specific shirt back and not a basic one. Luckily I got it back no problem.
I like the towel sprite idea since it lets you talk to NPCs with low Relationship while in the communal baths without wearing your clothes in the bath. I still remember talking to Hayden my first time in the bathhouse and I got him all passive aggressively mad at me cause I was naked. I'm over here confused, wondering why I'm getting heat for being naked in a communal bath? I'm surprised Hayden doesn't use the private rooms since he's such shy guy.