The claim for physician licensure is that it protects consumers from "quacks;" it is just a coincidence that licensure also reduces competition and raises doctors' incomes! In this case, the strength of licensing should be similar across states, and licensure requirements should determine whether a prospective doctor is competent, not whether a U.S. native or a migrant.
Recent research by Brenton Peterson, Sonal Pandya, and David Leblang (University of Virginia), however, finds the opposite:
Licensure regulations ostensibly serve the public interest by certifying competence, but they can simultaneously be formidable barriers to entry by skilled migrants. From a collective action perspective, skilled natives can more easily secure sub-national, occupation-specific policies than influence national immigration policy. We exploit the unique structure of the American medical profession that allows us to distinguish between public interest and protectionist motives for migrant physician licensure regulations. We show that over the 1973–2010 period, states with greater physician control over licensure requirements imposed more stringent requirements for migrant physician licensure and, as a consequence, received fewer new migrant physicians. By our estimates over a third of all US states could reduce their physician shortages by at least 10 percent within 5 years just by equalizing migrant and native licensure requirements.
Little evidence suggests that professonal licensure promotes quality or protects the public, but arbitrary discrimination against migrant physicians (many trained in the United States!) is particularly insane. As are all restrictions on high-skill (or other) immigration.