Doesn't sound like the teacher has done anything remotely unusual to me.
Teacher: Why aren't you doing your work?
Child: I don't want to.
Teacher: Oh, that's a shame. Is there a reason you don't want to do your work?
Child: I just don't want to.
Teacher: Ok then. But if you don't do it now, you'll miss your play to do it/do it in golden time.
I suspect the teacher did try to find out why your DD didn't want to do it, and was given the same answer your DD gave you.
"If the teacher had allowed her to sit quietly for a book or something she would have ended up doing the work anyway." How do you know that would be the case? I expect that your DD could have chosen to do the work at any time and didn't! If she had said, "I don't feel very well," then the teacher may have done that. Being met with, "I just don't want to!" is totally different!
You may not want to tell your child to do anything every adult tells her without question (and I wouldn't suggest you should) but I think your DD needs you to tell her that she must to do the work she is given by the teacher. Otherwise she'll be missing a lot more golden time in the future - which was her choice of when to do it. She could have done it when requested and didn't. Hopefully next time she'll do it when she should have.
Support the teacher/school and they'll support you and your daughter.