They can easily produce enough doctors, they just don't. A couple of reasons for this: schools inflate the amount of education required so they they can make more money and doctors go along with it (and a crazy amount of licensing requirements) to prop wages up by keeping the supply of doctors artificially low.

You could be an ICU nurse with 20+ years of experiences. Want to make a jumpt to becoming a doctor? You have to start ALL the way from the beginning of med school as if you an 23 year-old humanities major who decided to go to med school. Your 2 decades of hands-on medical experience counts for exactly nothing in the eyes of medical schools and certification boards. Does anyone really believe this is a good way to run things?

Fix the low pay and terrible conditions and yeah, you'll easily produce enough doctors and teachers, but late-stage capitalism isn't going to do that...