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You cannot really avoid the fundamental constraints - anywhere in the world, there are only so many doctors and so much money available for treatments. IDK if USA has a shortage of doctors, but plenty of European countries do. A country like Romania just cannot give its doctors big enough wages to stop them from seeking employment elsewhere, where they will get five to ten times as much (UK, Germany, Switzerland). As a result, local hospitals are seriously understaffed.
Where I live, having personal connections to good doctors gives you an advantage - you will be examined and treated faster. Then there is outright nepotism.
The outgroups are different than in America, but there are always people for whom the system sucks.