actually, statistics prove you wrong. Cuba pays surgeons roughly the same as streetcleaners but they have twice the amount of specualists per 100.000, compared to the united states (1). If you look at countries that have (almost) free education (like cuba), you see that these countries have similar numbers of physicians/specialists per 100.000 people. These facts tend to show that the main factor for having "enough" surgeons has nothing or little to do with pay and mostly with opportunity (free) and capability.
As an interesting sidenote, I'd like to point out that the high salaries of surgeons in the US help to prevent people from going into surgery.
Another point is that if you go into surgery for the money, I think you have the wrong incentives to be the best surgeon.
(1) https://data.worldbank.org/indicator/SH.MED.SAOP.P5?view=map...