Medicare also negotiates on a state based level and represents more people than most European countries.

Right now the US governments collectively spend more than most European countries per capita on health care. The states and Feds. Totally exclusive of the private market spending. Expanding Medicare/Medicaid may be great for other reasons but does not solve the underlying cost problems in the US.

Hypothetically, the amount of money that could be negotiated away is something like the sum of net incomes of US pharma/med device/insurance/healthcare, which is something like $100 billion annually. which sounds like a lot but it's only about 2% of annual $5+ trillion spend. You can't negotiate prices to be lower than the associated costs, the companies will just close up shop instead of being forced to take a loss.

At the end of the day, the fundamental drivers of high healthcare costs are (a) high labor costs of high-skilled doctors, pharmaceutical researchers, etc. (b) high cost of procuring land and construction of new hospitals in major metro areas. The first requires you to fix education first so that doctors etc. do not need to take out and later pay back what can now easily exceed $500k in combined tuition and living expenses. The second is politically unpalatable.