Here is a theory of why placebos work. I don’t claim that it is original, it seems natural enough that I am surely not the first to suggest it. But I don’t think I have heard it before.
Getting better requires an investment by the body, by the immune system say. The investment is costly: it diverts resources in the body, and it is risky: it can succeed or fail. But the investment is complementary with externally induced conditions, i.e. medicine. Meaning that the probability of success is higher when the medicine is present.
Now the body has evolved to have a sense of when the risk is worth the cost, and only then does it undertake the investment. Being sick means either that the investment was tried and it failed or that the body decided it wasn’t worth taking the risk (yet! the body has evolved to understand option value.)
Giving a placebo tricks the body into thinking that conditions have changed such that the investment is now worth it. This is of course bad in that conditions have not changed and the body is tricked into taking an unfavorable gamble. Still, the gamble succeeds with positive probability (just too low a probability for it to be profitable on average) and in that case the patient gets better due to the placebo effect.
The empirical implication is that patients who receive placebos do get better with positive probability, but they also get worse with positive probability and they are worse off on average than patients who received no treatment at all (didn’t see any doctor, weren’t part of the study.) I don’t know if these types of controls are present in typical trials.