One can easily imagine some weird data easily described by (and predicted by) very simple mathematical formula, but yet I don't consider this to be explanation. Something lacks here; my curiosity just doesn't accept bare formulas as answers.

I suspect that this situation arises because of the very small prior probability of formula being true. But is it really?

I think the situation happens because of bias. Demonstrating an empirical effect to be real takes work. Finding an explanation of an effect also takes work. It's very seldom in science that both happens at exactly the same time.

Their are a lot of drugs that are designed in a way where we think that the drug works by binding to specific receptors. Those explanations aren't very predictive for telling you whether a prospective drug works. Once it's shown that a drug actually works it's often that we don't fully understand why it does work.