That is absolutely not the "point" of modern homeopathy... The point of modern homeopathy is to spread a lot of nonsense about water with memory and other such bunk.
Secondly, you seem to have some funny ideas about the placebo effect. Placebos are used to try and measure peripheral factors. It could be that just going outside is what is curing the patient, and not the new drug you are giving them.... Or maybe spraying anything up the nose will help some symptoms, not the new nose spray you are testing. That's the whole point of a placebo...if your medicine is only working as well as the placebo, it's not working at all.
It so happens that additionally, sometimes you can get what is called "the placebo effect" where just the idea of being treated can help somewhat...but generally only in certain cases and for subjective things, like pain. It makes sense that people feel a little better subjectively when they are treated.
However, not all placebos cause the placebo effect and if a placebo helps it is not necessarily because of the placebo effect. Using placebos in the way you suggest is not good medicine, they are not reliable enough and require some dishonesty with the patient, a serious ethical concern. Furthermore, you should be able to get similar or better results from a variety of real treatments!
Outside of research, there may be occasionally a reason for a doctor to dispense a placebo...but overall they are not good medicine and neither is homeopathy.
> Yeah, it has no medicinal effect. But that does not make it worthless,
Actually, yes...that's exactly what it does. That's the whole point. If something only works as well as a placebo, it's literally worthless.