I don't share the broad opinion that you have to accept that situation silently. You clearly stated doing favours is out of the scope for this question. What me bothers is this:

> **They** were going to hire an assistant for this position, but **they decided** it does not come up often enough to justify the cost.[..] They [..] ask my department's director - **he** was OK with it

Although I personally would appreciate a nice 	diversification of my work, I can perfectly understand why this doesn't feel right. It's not about doing favours it became a matter of course. What really bothers me is that your director decided this without having a word with you. Furthermore the employees won't be treated equally. He decided that those tasks should be assignable to a limited set of employees.

As most people seem to find this acceptable I can't join that club. I imagine my boss saying this: "Hey, our toilets aren't that dirty at all. It's not justifying the costs for a cleaner. I've decided that our experienced women have to clean the toilets once in a while". Don't get me wrong there's nothing wrong in cleaning toilets.