didn't have to vs wouldn't have to

Hi, I'm desperate for help here. There is this exercise in a first certificate book where pupils have to underline the incorrect verb form in this sentence:
"Only poor women who couldn't afford servants didn't use to have to / wouldn't have to /didn't have to wear corsets"
I've got the answer key at the back of the book and the incorrect option seems to be the first one. It does sound funny to me but I really can't see why the first one is incorrect but the second isn't, when both of them are used to express habit in the past.
I'd really appreciate it if I could get some help here.

>didn't use to have to

As MM mentioned in his posting in the other thread, that's quite awkward for standard speech.

Both the 2nd and the 3rd options seem fine to me. I'd prefer the 3rd.  2nd is more tentative.