FAA regulates competition

A Dr friend of mine mentioned that he tried to apply as an AME with the
local FSDO and was told "we already have enough AME's go away". As a
capitalist, that really bothered me. Under what authority does the FAA
regulate the supply of AMEs? Certainly we can all understand that the
FAA must put requirements of AMEs (probably be licensed to practice
medicine, maybe take an FAA test or attend a seminar etc) but why do
they regulate the number? This may contribute to some areas having more
expensive medicals than other areas.
I've wondered the same question about DEs. Why doesn't the FAA allow
anyone who meets a very, very strict set of standards be a DE? Why do
you have to wait for a DE to die before the FAA will give you
authority? I just have visions of the Central Communist Committee
trying to figure out how much bread and milk to produce and what price
to sell it at. Regulating supply of resources doesn't seem to be in the
interest of pilots, safety, or anything else other than giving some
people pricing advantage.

-Robert