Could you be more specific what is a lab setting for you? Natural experiments are not what I meant when I spoke of experiments, as natural experiments are observational inferential methods!

btw did they ever tell you about that physics experiment in a lab that was built just over a subway line? So much confounding!

Jokes aside, your assumptions amount to assumptions about what "controlled" and "in a lab" means. I hope you see it makes more sense to define the requirement for experimental identification mathematically, in which case you'd see that the conditions are not different in kind, only in degree. etc.

Edit:

If that counts as revealed preference data, I can assure you that econometrics are used to great effect in pricing, auctions etc - one of the reasons certain orange and blue companies hiring experts on this have become mucho rich in the past couple of years. Some oldschool econ models may not be the best to describe the altruistic, boundedly rational present-preferrer. But oh boy, can you make some serious dough if you can mechanism design the auction platforms and the best the firms can do is to try to train some machine learning models against it.

There is a substantial difference in degree when dealing with atoms, molecules, homogenous materials vs. people who think, face incentives and understand game theory.

As far as economic reasoning goes, there are some studies you can do (like optimal auction clearing) where you can hold the inputs equal and then adjust some aspects of the optimization (the objective, constraints, or decision variables) and get a very accurate picture of how market changes would impact the results. I think that is probably an exception rather than the normal case though.

In general, my thoughts during my studies has been that the economic theories of supply & demand, incentives, elasticity, theory of the firm, game theory, government intervention...etc all has more use as a generic framework of thinking (ex: if we put in a price cap, here are the expected impacts), rather than an equation I can use to get an exact answer (basically exactly what you're saying above). Doing some kind of analysis on things as complex as the US economy must have massive inaccuracies involved as there are too many factors and even behavioral economics doesn't have all the answers for why people don't always act rationally.

So how do you confirm these first principles? I'd argue that those are an even wider door to let your biases flow into the analysis. I mean this type of argument has given us trickle down economics which has significant real world evidence it doesn't work.

For example people use says law to argue saving does not create unemployment but says law can also be interpreted as saving is impossible over the long run and therefore unemployment shouldn't happen either.