That's not how it works. The process of becoming a doctor is much more formalised than you seem to insinuate and mostly does not depend on a single individual or a group of individuals other than indirectly.
I do agree that some doctors have a Messiah complex and are self-important to the point of absurdity, but they still mostly tend to do a good job.
I would argue that the limiting factor of why there is a general shortage of doctors and nurses is that the job is not the easiest one, physically or mentally, people tend to work long hours and awkward shifts and the education itself is challenging and long.
