How we've ended up regulating medicine to the nth degree, but when it's teeth we're like "oh well, lol", continues to mystify me.
I see what you mean.
But I'm a computer programmer, and if someone asked me to find a top quality academic study proving, beyond a shadow of a doubt, that it's a good idea to indent your code - I couldn't point you to one.
Not only is bias introduced from accidental collection flaws, it’s also often tampered with intentionally cherry picking data, choosing interesting data or in some cases flat out falsifying data. In addition, evidence based reasoning often suffers from there being a lack of evidence to make a decision from. Or in some cases some critical aspect surrounding the decision is very niche to the case so the data may not take that into account unless it’s highly tailored data (evidence based reasoning tends to focus on breadth of applicability because gathering evidence is a long and often expensive process).
There’s still a lot of place for using theory and reasoning in conjunction with or in absence of data. Things like experience, professional opinion, etc. Medicine should be no different in that regard to any profession. The key is of course to always strive for sound empirical evidence/data where possible, but to use sound documented reasoning and theory in its absence if you want the best objective results.
It's even more amazing to see this at play in domains that are directly tied with your well-being, where there's abundant anecdata, but people are holding out until very long and very expensive research have made a pronouncement. Like, thousands of people claim this particular herb is {$positive_claim}. I could try it for a week and see for myself, but I think I'll hold on to my 10$ and wait until research confirms this by the time I turn 90.
Another aspect of this fallacy is nicely highlighted by the aphorism Not everything that counts can be measured. Not everything measured counts.