Basically you have a tax by another name.

That's not necessarily a problem in and of itself, there's plenty of areas in life where we have essentially a tax by another name or system. The problem I see, looking from the outside from a country with a "universal" health system, is that the American way of doing it is extremely complex, which pushes up the price of everything. It's not that there are profits involved, it's that there are so many incentives, and then patches to prevent them, generating more in other places.