If I had to pick one, I would say heterogeneity of insurance plans as most fundamental.
Consumers must have some exposure to cost savings or liability for downward price pressure exerted and inferior substitutes to be selected. People will never pick a $20 treatment over a $20,000 unless they have skin in the game, even if it is 99% as effective.
I think this has to be instituted at a insurance policy level for a number of reasons. Charges are stochastic and in the future, while policy premiums are predictable and immediate, allowing consumers to see cost or savings across the entire policy and pre-commit.
Measurability is tough on this because it amounts to allowing inferior treatment, and I dont think this could be papered over, even if it brings down the price of all care and allows more treatment in aggregate.
Uniform pricing is much better on the messaging. It is adjacent to collective bargaining, just mediated by a market instead of a technocrat. It can be sold to the left as an attack shadowy rentseekers. It can be sold on the right as a free market reform. On the pragmatic front, it can It has a transparent pricing angle, where you could see prices, which current transparency legislation seems to fail. I also think there is a lot of negative will pent up about negotiated pricing and the idea of companies paying drastically lower prices than an individual because they can throw their weight around when bargaining.
"Remove the people between you and your doctor."
In all socialized systems the government decides what your doctor can do, 100% of the time. Of course from a patient perspective it looks much less restrictive, but that's only because your doctor never brings up treatments that aren't paid for.
One of the big issues with the US system is that the patient is put right in the middle of the decisions so sees all the rejections, has to deal with all the paperwork, and pays the price when things go wrong.
This is the admittedly huge emotional problem, but distinct from cost problem. Hospitals and insurance billing systems can be as dysfunctional as they want because all of the financial liability is outsourced to the patient.
If this outsourcing were not possible, insurance and hospitals would have worked the issue out long ago. I expect all treatment would be pre-approved by default, and hospitals would carry the cost of misbilling (like how a retail store eats a fee for credit card purchases)
Patients need to be more involved.