And yet when people really want quality health care, and fast, they leave whatever worker's paradise they live in, and come see and American doctor.
No, they generally do not. And the numbers suggest it's not very smart for people in "worker's paradises" to do that, since the health outcomes, negligence, and error rates are (for most people) measurably better in socialist medicine systems.
Saudi billionaires do go to the US, along with various other billionaires - that's because money is meaningless to them, and if you have an income of several million dollars plus, there is indeed very good care available in America. Probably even the best in the world.
But how relevant to 99 percent of the population is that? You need to be on the Forbes 100 richest list to get that kind of care, literally. Any income bracket below that, and you're dealing with a medical system that delivers poorer service at higher prices than most socialist systems.