The placebo group is called such because it receives the placebo treatment, not because medical researchers think all improvement in it is attributable to the placebo effect.

Sure. But 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).

You are correct in that most intervention studies don't care about the magnitude of the placebo effect, they just take the placebo arm of the trial as a baseline. But that doesn't mean that we couldn't or shouldn't ask questions about the placebo effect itself.