Yeah, don't take Switzerland as some example to follow on healthcare. Having to blow 300-400 francs a month in insurance is one of the biggest political issues at the moment, it is second to only the US in terms of how expensive it is.
To add to that, the world class treatment that people get mostly occurs in public hospitals.
For one, Switzerland's system is still highly rated in Europe. I think your answer might be a result of your general expectations no? Compared to the American system, Switzerland is a world class system.
The reason I favor continued insurance premiums is that they, by definition, price risk appropriately. They assess each person appropriately and assess how much of a general risk they are. For a lot of reasons, we shouldn't penalize people with genetic diseases and diseases unrelated to lifestyle choices but for again, a lot of reasons, we SHOULD price in premiums for people who have horrible lifestyle choices.
There is still no such thing as a free lunch. We can reduce costs, shift costs around, and create a managed pool but still, no such thing as a free lunch and we should be cognizant of that when offering people benefits. Human nature being what it is, they will maximise their benefits accordingly with the least adjustment to their personal lives. This, to me, presents one of the biggest reasons with socializing medicine.
Also, the American system rewards healthcare innovations which are used by other universal healthcare systems around the world. Socialized systems are not conducive to innovation to reduce costs, and not conducive to creating an incentive to further the technological advancement that we have seen in the American capitalistic healthcare system.
For note: the NHS is experiencing considerable costs related to this issue (not as much as it has been said, but still).