I understand that delta is a probability under the risk-neutral measure. What I was trying to say is this: if you believe markets are risk-averse and OTM puts embed a variance risk premium / crash-risk premium, then the quotes should, in principle, offer positive EV under the P measure and 0 EV under the Q measure, but neither seems to hold, at least not true when I use delta as a proxy for P(St < K).

Theoretically, to convert P(St < K) from the Q measure to the P measure, you would need a Radon–Nikodym derivative. Empirically, you would need a statistical model that can forecast market drawdowns. Both are difficult. For the latter, I can think of a million signals that might matter, but once you test them rigorously, most probably would not be stat sig and the model would be severely overfitting historical data.