So I'm not the only one who can't get a doctor to go around researching his stuff?
Nope, you aren't.

Mine will study on their own (usually) to get from trainee to adept-after that, I have to micro-manage what they do in order to get them to do anything other than eat or relax in the pond.
I had no idea the sick ones went to the hopsital. I never see anyone in mine other than the occasional builder repairing it.