Government is in theory incentivized to reduce costs because it has limited funds. The thing with healthcare is that the purchaser, if private, pays whatever (s)he can afford (how much is your health worth it to you?). Whereas if the state is the purchaser, it is (a) A monopsony, having substantial power over healthcare providers; and (b) Doesn't care as much about any individual patient, thus being able to make decisions that are rational on the aggregate level

On short: much better to be a healthcare provider in US; much better to be a patient in EU.

Do you think the same downward pressure on costs applies to schools? What about fighter jets?

The demand for healthcare is infinite. Even when there are marginal improvements in treatment, patients and physicians want the best.

The ability of national health systems to say “no” is one of the big levers to controlling cost, in the US, that control is quite fragmented.