a profession as wealthy as medicine needs the taxpayer to fund its training is preposterousMost doctors already come from wealthy families (specifically, they have doctor parents) because in addition to the tuition of medical school, there are a variety of other expenses (board examination fees, the undergraduate requirement, interview expenses for both medical school and residency) that are difficult to fund without assistance. Also, compensation for physicians is not what you seem to think it is outside of subspecialized fields, and the expense of medical school (and the opportunity cost of residency) means that physician shortages in the general disciplines will only continue to get worse as medical students realize the only way they can pay back their loans is to subspecialize.
Also, medical schools are primarily limited by number of faculty, and it's difficult to find doctors for med school faculty roles... because they're so poorly compensated in comparison to other opportunities.
If you want more doctors, first provide incentives for doctors to teach, then provide funding for those who normally don't see medical school as an available opportunity, then incentivize people to go into general disciplines, then properly compensate residents so they're not throwing away ten years of potential income, then complain about how "doctors are overpaid but there's also a big shortage of them".