I don't see a problem with health insurance companies "making a profit at the expense of someone's health" -- provided people feel they have an option to not buy the insurance or find a better alternative.
I've said something similar to this on this thread, that there is a divide in the USA between rich and poor -- a divide which is bigger than other industrialized countries. We already have Medicare and Medicaid for the elderly and the poor, respectively. One simple thing we could do, I suppose, is boost funding for these, so more people are covered, but then the money has to come from somewhere. We can either raise taxes (which would be resisted) or cut some other programs (the military is a possibility). One thing we cannot continue doing is borrowing trillions of dollars.
I don't think it's fair to call the private insurance companies evil. Everyone can read the contract and refuse it. However, the powerful influence they have over politicians is a serious problem for crafting alternatives.