I'm not convinced that's true. We still have private healthcare in the UK; even though our health care is also free to everyone. People like to immediacy and convenience of private, and choose to pay for it, even when there is a free option. Private doesn't go away.
While technology is important, don't you think the US spends (compared to everyone else) too much on technology? Most of the illnesses don't need the newest or 'state of the art' devices. What they do need is doctors, accessible and FREE to people. Technology doesn't trump that (lol).