I think one of the points of this entire thread has been to make it clear that "it works" only applies to people who have money, which means of course that it doesn't work.
Universal healthcare actually means a downgrade in the experience for these people, which is one of the reasons why they don't want it. Yea, they might want to make sure that people don't get sent to the poor house just because they came down with some random disease, but god forbid they have to wait their turn behind some plebe in the doctors office.
But it also means a much higher cost. I know these people are wealthy, but they are getting fleeced. Many (all?) socialised systems also have a private system along side, so the wealthy can avoid the great unwashed.