I admire your optimism in epidemiology. In point of fact, though, we have a rough natural experiment in the form of a food that doesn't cure a disease, but rather makes half of all drugs worse. That's very valuable knowledge, and under ideal epistemic conditions it might have been discovered within a few years of organized drug discovery as such. Yet was not widely known until the 1990s. So that's a failed positive control, which suggests that our practical capabilities to detect these kinds of effects are limited. Understandably so, given that there is no general requirement for dietary logging in clinical trials.

That said, "a food that cures cancer when eaten" is not the bar for experimentation. More realistic might be something like "a dietary or behavioral protocol that, in some way, ameliorates this or that indication".

For organisms with our body plan, "a cure for cancer" is like talking about "a cure for defection". But clearly there's "stuff that is efficacious against particular instances of cancer", a lot of which we found through techniques like natural product screens, i.e. "just trying stuff", rather than via rational drug design.