Which control? Placebo control or no treatment control?
If you set up an experiment with Homeopathy, placebo and a no treatment control group, then its been well proven that the results for the placebo and homeopathy will be pretty much identical – the problem for your argument is of course that in most cases those outcomes *are* both statistically better than the no treatment group, often by a pretty large margin!
Therefore your argument that “it is having no effect” isn’t a scientific viewpoint, it’s emotional, non?
I suspect that you are misunderstanding scientific method.
In your proposed experiement, placebo and homeopathy are confounded in the ‘homeopathy’ group.
The ‘homeopathy’ group is essentially a second placebo group: any impact of homeopathy relative to the ‘no intervention’ group is due to it being a type of placebo rather than the action of homeopathy.
Statistically, all the experiment shows if that two different types of placedo are more effective than doing nothing.