As a person who has lived in Spain, UK, and now California, I can attest to one thing: the quality of care in California (I can't speak for the whole country) is vastly superior to what I received in both Spain and UK.
Sate-sponsored universal healthcare is amazing, I love the concept, but it also means that they have to run it like a very stingy HMO. They have a rulebook and they go by it, if your case is even the slightest out of their parameters, tough luck. And don't you dare ask for a second opinion, you'll get the doctor that has been assigned to you and accept whatever they tell you. I could bore you with countless stories of doctors who have used tricks not to provide service and make it look like it was the patient's fault.
The problem with private healthcare is that profits corrupts it. The problem with public healthcare is that politics corrupts it. There is no good solution.
Yet, living in Germany, the problems I hear about our healthcare system from friends or in the media are an absolute far cry from the insanity that I hear about the US system. Maybe some of it is sensationalism, but I very much doubt that would account for the whole story.
I'm sure there is a lot of nuance but long term healthcare outcomes are generally lower in the US compared to other countries. https://www.healthsystemtracker.org/chart-collection/quality...
There are other public healthcare models besides Beveridge though. Some countries do the payment & financing via gov, but the actual service is a mix of public/private. Not a perfect solution, but in my opinion better than what we have now. Maybe more achievable than Beveridge too.
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).