Earlier quoted context omitted.
It is clear that you have not even read the Vedas to understand its implications on the world, especially in science. Most of the statistics that you ask have been lost due to them being so old, or deliberately destroyed. But we have the results to prove that these existed. "Strong observations & correlations" are just another way of saying "trial & errors". Not just ayurveda, but take any science or even Mathematics…
Look, you obviously have an axe to grind. And you are conflating too many different things. So I'll limit myself to the original point. Science, particularly modern science, even with all its baggage and flaws and politics, is evidence based. Evidence in this case is statistics and data. Those are not present, from many reasons (as an aside, I don't think there is any evidence of statistical trials being performed in…
> Science, particularly modern science, even with all its baggage and flaws and politics, is evidence based.
Can be reworded as: "Science, particularly Vedic science, even with all its baggage and flaws and politics, is evidence based." The vedas are not any different than any sciences that mankind honestly developed. Only, it goes far beyond what we (aka modern science) are/is able to comprehend, about the consciousness of the universe etc. With time, that will also be rediscovered. Also not to take away anything from modern science, many things have been discovered & invented far more than Vedic sciences. My problem is treating the Vedas as purely a religious book like the Bible & Quran and neglecting the great expanse of knowledge in it.