By that logic, we should artificially cap everything. Why allow just anyone to be a programmer? Don't we only want the best programmers to write our software?

Any entrepreneur should be able to open up a licensed medical school. Anyone who graduates should be able to get certified as an MD. This is how markets should work - not capping doctors on the hope that we get "better" ones.

Also, I have seen some awful doctors, so I'm not sure the system is working.