There are exceptions when there are rare natural experiments (e.g. I forget the country, but the European one where some issue caused all flour for the country to be only whole-wheat, which led to clear nutrient deficiencies due to the phytic acid there) but in general there are way too many confounds, and measurement is far too poor and unreliable (self-report that is not just quantitatively but qualitatively wrong, and you can't track enough people nearly long enough), there is virtually no control whatsoever (diets and available foods shift considerably over just decades), and much of the things being measured lack even face/content validity in the first place (e.g. "fat" is not a valid taxon, and even "saturated vs. unsaturated" is a matter of degree).

We are missing so much of the basics of what are required for a real science here I think it is far more reasonable to view almost all long-term nutritional claims as pseudoscience, unless the effect is clear and massive (e.g. consumption of large amounts of alcohol, or extremely unique / restrictive diets that have strong effects), or so extremely general that it catches a sort of primary factor (too much calories is generally harmful, regardless of the source of those calories).

But even setting that aside, you can't define or study "Mediterranean diet" rigorously even in RCTs, so I don't see how you can think you are going to get much of anything here from epidemiological work that is going to lead to anything practically actionable.