Oh, sorry, one other idea.
Is the reason you don't like the tub something mechanical about it? Is it defective in some way? Maybe if you tell the landlord that the tub isn't nice to use, the landlord might replace it. Maybe the landlord just doesn't know that the tub has problems because the landlord doesn't bathe in it. Maybe the tub once was great but now is outdated or worn out in some way.
If the tub is technically fine, and you don't like it for some unique personal reason, this probably wouldn't work, but if the tub is in any way defective, the landlord is responsible, after all, for correcting the problem.
Just a thought!