Doesn’t the fact that vastly different systems perform better than the US possibly suggest that our problem is something other than the payor model? What is the theoretical reason why US costs would be higher than Switzerland? Premiums for private insurance should be much lower in the US, given that Medicare takes high cost people out of the private pool.
The US hasn't had compulsory private insurance up until about 10 years ago. Before that costs were going up even faster[1]. Even then if your employer is providing your health plan the amount of "shopping around" you can do is limited - most companies have 2 or 3 options (a PPO, an HMO and something with an HSA). This leaves only the uninsured (i.e. the poor) or previously uninsurable (pre-existing conditions) in the actual open private insurance marketplace. It's not surprising that premiums there will be crazy high and it's not really that close to being the Swiss model.
> our problem is something other than the payor model
I partially agree with that - the payer model is one facet among many. There are other problems with healthcare in the US. Hospitals can veto opening of competing hospitals in the area, complex billing, not enough residency spots leading to a shortage of doctors, whatever the F is happening with prescription drugs etc. GP was only asking for alternatives to employer healthcare though.
The difference between Switzerland and the US is that in Switzerland pricing is regulated. The free market does not work when your life is at stake. You can shop around as much as you like for a butt enlargement and skip it if it's too expensive, but if you find a bat in the bedroom you need a physician straightaway, and then he will overcharge you.
There are some procedures where shopping around is conceivably an option.
Once you're in desperate need (say, when it's bad enough that you're calling an ambulance), or unconscious, it's not realistic to suggest price-shopping.
Markets of the mostly-free sort work well enough for commodity products, like the kind of peanut butter you're buying a jar of every few weeks (though even that's regulated, from things to food safety to nutrition labeling); for everything else, government's a fabulous tool to make sure people aren't taken advantage of, whether it's through heavy regulation (e.g. Switzerland, as someone mentioned) or offering the service itself (e.g. UK).
The vast majority of health care is a commodity product. Unless you have some super rare condition, whatever your problem happens to be it's extremely likely to receive more or less the same treatment from a large number of potential providers.