Supply and demand curves aren't observable: only their intersection, price, is observable. The curves also move about in unpredictable ways. So we've got this situation where unobservable quantities move with unknown dynamics in a noisy, unpredictable fashion.

In order to get anywhere with a statistical estimation problem as hard as that, you have to impose a lot of prior structure. I'd be surprised if, much of the time, you didn't end up effectively assuming the answer you want to see.

I'd go as far as to say supply and demand curves are a pretty useless abstraction. I've watched two economists argue over whether the 2015 oil price slump was a supply shock or a demand shock: if they can't get that right, what hope do the rest of us have?