I usually feel both mentally and physically relieved once I have visited a GP.
You're quite right, that is exactly the placebo effect. And you are not alone in feeling that.
The first time we experience it is when we fall as a baby & mum "kisses it better". It doesn't make the scraped knee heal, but it usually stops the crying.
Richard Dawkins uses the doctor effect as an example of the placebo effect himself in The God Delusion
But many's the time I've been instantly "cured" of some minor ailment by a reassuring voice from an intelligent face surmounting a stethoscope.
You trust that what ever is wrong with you is going to be sorted out. Of course that is going to make you feel better.
Sure, I agree with you that the red pill can relieve stress or tension & that perhaps the patient may not be able to relax by themselves without an intervention, even if it is a placebo intervention. And stress relieved (no matter how its achieved) has a genuine physiological benefit on the body.
I think what I was doubting that a red pill by itself (with no rest) would be as good as red pill + rest. Although I suppose that might depend on what the underlying condition is in the first place.