I also do not recall women doctors in Gemora, mostly witches or similar type healers.
Halakha requires women to not be idle. In good old times, women spent time doing necessary work of laundry, cooking, carrying water, making clothes, and teaching kids manners and emunah. due to our sins of insatiable curiosity, men invented lots of machines that wash clothes, microwave food, and make clothes; kids are sent to school at early age to learn alef-beis and not to listen to parents. In response, women raised their standards of required home cleanliness, fashions, and food quality. Good. Now, we have illegal immigrants doing the rest of the chores. What are women supposed to do? The only remaining task is to teach kids emunah, but kids are at school. They can’t be reading CR the whole day.
One side effect is that in some communities the only accepted job is teaching. This is good as it creates a pool of cheap teachers, as it should be (same was true in pre-industrial US in general). But then some who do work as teachers do not really want to do it, but have to. And this crates terrible effect on kids. Merit-based hiring could solve the problem, but often prevented by preference for hoshuve families.