But s/he needn’t have a B.Arts in management to apply to med school first.

I don’t know what you mean by “Maybe a few hundred”. Do you mean schools or neurosurgeons?

If 1., there are only 150 med school for all Dr. in the US, contributing to a very low number of Dr. Per capita.

If 2. They study medicine. Do residency. And train on the job for the rest of their lives... just like today [0]

[0] actually one of the reasons for medical errors, a top three killer in the US, is that most Dr. don’t update their knowledge one thy finish their residency. :S