No the US is a terrible example, its an absolute outlier.
The US mix according to your graph appears to be about 50/50 what’s wrong with that? Is it a ‘terrible example’ because it completely undermines the point you’re trying to make?
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There are plenty of good examples of private sector involvement. France and Germany spring to mind.
According to jambalaya’s graph the ratio of private to public involvement in healthcare in France and Germany is very similar to the UK, ie, a bit more private involvement but also a bit more public involvement.
A high level of private involvement doesn’t necessarily mean better healthcare, it can just mean that the public healthcare provisions are crap.
I reckon the US model shows this particularly well. The astronomical healthcare costs in the US also shows what can happen when you factor in profits and all the administrative costs associated with that.