You do make one mistake: assuming insurance companies would go away. They wouldn't be the monstrosities they are now, and there wouldn't likely be as many, but there's no praticular reason for them to go away unless your universal health care covers abolsutely everything; many examples don't.

For instance, up here in the People's Republic of Canuckistan, emergency dental--I just got a puck in the mouth and will require surgery, to use one type of accident--will usually be handled by the normal system, but run of the mill dental care; getting a cavity filled, cap for a broken tooth, and so on, isn't. So my employer has dental coverage, and for that I deal with the insurance company (and the brief exposure I had to that makes it quite clear I don't to ever deal with the current American system for more important matters).

Similary, I get extended drug coverage in case I need something beyond the scope of the government system, insurance for things like braces, and possible prosthetics, which may or may not be covered under the government system, and so on.

We do have insurance companies up this way, and they do make money. Just not the hand-over-fist amounts they do down there.