the question under discussion here is what actually is the placebo effect and how much of it can you attribute to psychosomatic factors and how much to just regression to the mean (aka natural healing).

In that case your opener is slightly polemical :)

But that doesn't mean that we couldn't or shouldn't ask questions about the placebo effect itself.

Agreed. The problem with nonintervention arms for studying the placebo effect is that there aren't clear incentives for adding them and they cost statistical power.