You point at some facts that happen to be similar (when adjusted) for the US and Switzerland, but it's rather arbitrary. What the hell does gun ownership have to do with healthcare? And of course, like most industrialized countries, there are "lots of cars"...
The absolute difference in wealth doesn't affect just medical equipment, it affects practically everything besides labor. One of the reasons why labor is so expensive is the high taxes (VAT etc). When the government subsidizes that expensive labor, it'll get a big part right back.
You also edited your post to agree more with mine (i.e. Obamacare), when the original point was more like "private insurance can work look at Switzerland!".
Yes, it can work, if you're wealthy Switzerland and you regulate the fuck out of everything. Touche...