I followed what your argument was, but would be interested in seeing you pursue it. From what I can tell, there isn't much evidence that an advantage in preventative care makes up for the gap between Cuba and (say) Spain on major health event outcomes. For example: you're roughly as likely to die of CVD in the US as in Cuba, with CVD being seemingly a pretty good proxy for preventative care overall.
If it's not preventative care that Cuba does particularly well, what is the thing it does well? There would need to be something, right? One of the major tasks of the health care system is to prevent people with CVD, stroke, and cancer from dying. Cuba doesn't do a particularly good job of that. I'm sure there are other things a health care system needs to do well. What are they? Then we can go find out how well Cuba does them.
If it's not preventative care that Cuba does particularly well, what is the thing it does well? There would need to be something, right? One of the major tasks of the health care system is to prevent people with CVD, stroke, and cancer from dying. Cuba doesn't do a particularly good job of that. I'm sure there are other things a health care system needs to do well. What are they? Then we can go find out how well Cuba does them.