There is a limit put in place on supply (seats at medical schools) already. Weeding out is part of that system already. The question is should cost be part of that.. we decided somewhat yes which is fair if you decide to limit supply in the first place.
To limit supply is mostly to control price, like how OPEC controls oil. Current doctors have a vested interest in remaining a scarce commodity and lobby accordingly on the boards it matters.
The actual limit is residency slots. Every year there are many students who graduate from medical school but are unable to practice medicine because they can't get matched to a residency program.
Yep, that's the true barrier to entry. The main issue is there is that Congress has capped the Medicare funded residency roles to the same number since 1997 (Balanced Budget Act of 1997). In that time period, the US population has grown 21%.