I don't think 'want' is a word you are looking for. Mixing services are employed to sever a connection of transactions at a particular point, making the user somewhat anonymous again since the trail is already convoluted or tainted with lots of in-betweens. They are receiving fees for the coins that they mix, and they do not have control on whatever coins they receive in the process, so it's not really uncommon for them to receive coins that are tainted with illegalities but still accept them since that is what their service is for.

I mean, if I am an anonymous entity hiding in the sidelines and someone wanted to trade his/her stuff with mine in exchange of a small sum, why shouldn't I do it?