My dad, in the US on Medicare (one of the government funded systems), was denied a test. Because we have the option and had the money, he went and got the test himself on his own dime. That kicked off a series of events that led to a quadruple bypass, avoided an impending heart attack, and likely added many years to his life and his ability to remain and functioning member of society.

While I love the idea of never having to think about health care costs for a variety of reasons, I do like that some services are available to anyone with a wallet and not locked behind government controlled gates.