I think this is a good example where the usual association government run = bureaucratic ; privately run = straightforward breaks down because bureaucracy/non bureaucracy is not a function of the economic model but that of the inherent simplicity of the model. One of the reasons why many soicialised systems of healthcare are 'simpler' is because they have universal coverage which means that the whole process of checking who is eligible to see a doctor, does their plan cover this doctor, did they pay their premium, which treatments they are eligible for, how much of their spending limit they have exhausted do not exist because everyone is eligible and everyone is eligible for everything. It is like going to an all you can eat buffet and wondering why is no one writing down what I am eating :-). I could add more examples to it e.g. If all surgeons are paid a fixed salary there need not exist an infrastructure to count how many stitches they applied this quarter and so on..

Yet, we do track most of these metrics. Doctors are paid on work done and don't have fixed salaries, GPs have overly complicated spending limits on various resources, and so on. Checking patient eligibility alone can't explain an additional $5000 cost per patient and year.

You may have misunderstood. I was not trying to explain the $5000 gap. Administrative costs is one example of the cost difference. Research shows that 'socialised' health systms spend up to $ 800-900 less per patient per year on admin. (I think it was diff between USA and Canada) I am not sure of other systems but in NHS England there is no tracking of actual number of patients seen in primary care and details of each patient's complaint. The last audit done on that was over 5 years ago which was also based on data sampling and no such audit is currently planned. There are other reasons for high cost - one of the is the list pricing of actual products used (socialised systems pay less for products, UK pays about 20% less for pharmaceutical products than many other industrial nations). UK consultants and surgeons are not paid for how many procedures they do, 'coincidentally' UK surgeons operate less frequently. I am sure there are several other reasons that explain the $5000 gap but these are just a few.