I think this is mostly a problem with state funded healthcare budgets being cut (relative to population demographics) in these countries. If the UK or Spain spent anywhere even close to what the US spends on healthcare (per capita), I have no doubt that it's healthcare provision would be just as good. In the UK, healthcare provision was notably dramatically better 20-30 years ago under the same system (except for less private finance).
I don't think so. With state funded healthcare you get rigid rulebooks and policies. In the capitalist-ish US model, if you are a successful advocate then you can get better than average care because there's enough flexibility in the system (in many cases, physicians can individually decide to over-extend for one patient if they choose to) to allow for this. Having a private payer market absolutely helps here.
The problem is that it always happens. There's no such thing as comparable funding.