Most of the problems of the US system aren't really a matter of who pays, but the fact that so much is paid for services, at every level. Any really significant savings, cutting bureaucracy and pressuring providers to make costs resemble those of other developed countries, are taking money out of someone's pocket. Many hundreds of thousands of them, if not millions. This makes any significant reform very difficult, as those people vote, and will know exactly who made them worse off, even if the country in general was made much better off.

Read The Logic of Collective Action by Mancur Olsen. It wasn't written thinking of healthcare. but anyone looking at the US healthcare system will see that what is going on is stacks upon stacks of collective action beating overall societal efficiency, over and over and over again, in such a way that it's basically in none of the decision makers best interest to actually increase overall efficiency.