> every inhabitant of a country is entitled to that excellent healthcare

This isn't always true..

In some of these free healthcare countries you can be SOL if you get cancer or a rare condition and don't have money for the latest treatments. Here in New Zealand the wait times are so long that a lot of people just pay for private surgery/screening. My father for example was out of work for almost a year waiting for a hip operation, he irrationally thought he was getting a good deal having it publicly funded.