Civil law and criminal law are different. If you don't pay your student loans and stay in the US, the government can ruin you financially, but can't put you in prison. Why do you think they'd be able to extradite you? There's no reason that I can see that you couldn't even get away with walking away from those loans, moving out of the country, and coming back to the US to visit whenever you wanted using your US passport. As long as you don't actually have any financial assets under US jurisdiction, what could anyone do? You'd still have to file US tax returns on your worldwide income though if you kept your US citizenship. Tax evasion is a crime.
However from both an ethical and practical standpoint this is all a very bad plan. Ruining your ability to have any sort of financial existence in the US to avoid paying loans that you'll easily be able to pay doesn't make much sense. If you ever wanted to move back you'd be in a world of pain. The only time I could see this being something people would actually seriously contemplate is if they wanted to move forever to a country which pays doctors a lot less such that you couldn't afford to pay your US loans off. And even then, it's still morally wrong.
