We should continue to license doctors until we reach the point where the marginal benefit of additional medical care (assuming a negative relationship between quantity and quality) equals the benefit of no additional care at all.
But I am guessing there are some pretty big threshold effects--that there might be large discontinuities as one maps qualifications to outcomes. You really don't want a cardiologist who keeps just missing veins and you don't want an internist who can't quite get the drug interactions right (just as you don't want a 747 pilot who just misses the runway 1 percent of the time).
I think one of the ways economic analysis gets us into trouble is when we rely on continuousness in production and utility functions. Even worse is when we linearize around points--and that perform large comparative statics experiments based on that linearization.