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?
In all fairness, you are wrong
about your first argument. Both demand and supply curves are empirically observable through auction mechanisms and market reaction tests.
I'd be happy to forward you to research on them if you are interested, but don't try and pose opinion as fact if you aren't in the field.
In some cases I agree that an auction will give you an estimate of what demand or supply would look like at different prices. Northwestern university used an interesting variant of a Dutch auction to sell its sports tickets:
But auctions are often impractical. Auction mechanisms that induce participants to bid their true preferences are complicated, and you're still forced to assume that the auction participants behave rationally and optimally.
In general, the point that I'm trying to communicate is that it's very difficult to disentangle supply and demand: much harder than most people realise.
I think OP was stating that they aren't measurable in the real economy, not that we can't construct situations in/mechanisms by which they can be observed.
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?