It's a difficult fix, because the real issue here isn't who pays, but how much it's paid, total. If the cost of care in the US was the same as the cost in, say, Spain, the vast majority of people would have little problem paying out of pocket, and having just high deductible insurance for really big ticket items. At the same time, it'd be easy to have the government pay for it all. The US system is just very expensive in general, so it's a problem regardless of who pays for it.
Most of the costs are ultimately salaries to Americans, and money handed to American companies, so most savings would come from someone's livelihood. That's why we cannot reform: The party that actually cuts costs will build resentment for decades, and create a blip of unemployment. Nobody wants to do that, and therefore you aren't going to be a serious, relentless attempt at cutting costs. We've seen how the attempts that the ACA made were counteracted by consolidation at all levels.
Serious cuts have to have no mother. Say, if we ever did have an AI that worked well enough at this, and outcompeted primary care physicians. Foreign pharmacies bypassing all controls and being able to hand you much discounted drugs the day after. Telemedicine and cheap travel put together to make surgery that didn't involve an ER visit just as easy and much cheaper than using the US system. Straight out disruption, because the incentives are such we sure aren't getting improvements in regulation.