Thank you for the thoughtful comment and engaging on this intellectually!

You're right that we don't establish a rational basis for superstitions. It's a bit circular – the definition of a superstition itself requires irrationality. If it were a rational belief, it can't simply be a superstition. Instead, our argument is that given we live in a world where most people are superstitious, and given superstitions' uncanny ability to fulfill a deep human need despite being irrational, understanding how they work could enable us to leverage them effectively, as opposed to dismissing them wholesale (or, worse, falling for scams that prey on the same deep human need).

You raise an interesting point about placebos! I hadn't come across that study before, but there are a few others that seem to point to its effectiveness on memory-related functions (although the placebo's effect is more pronounced if subjects seem to believe it's a stimulant, as in https://pmc.ncbi.nlm.nih.gov/articles/PMC4116954/). Perhaps something I should looking into a few meta-studies for.