As America doubles down on government authority over health care, Europeans with the means to do so are increasingly circumventing their own centralized systems. In Britain, even though they're already paying for the National Health Service, six million Brits—two-thirds of citizens earning more than $78,700—now buy private health insurance. Meanwhile, more than 50,000 travel out of the U.K. annually, spending more than $250 million, to receive treatment more readily than they can at home. Even in Sweden, the mother of all welfare nations, half a million Swedes now use private insurance, up from 100,000 a decade ago.