What's wrong with the following example:

Homeopath examines 150 patients all suffering from the same complaint.

Homeopath chooses to prescribe different remedies to some people based on something he/she sees in them that conventional science might ignore.

Patient is assigned a remedy and told how to take it. They are not told what the remedy is called so they can't look it up. They are not told how it works for similar reasons.

Pharmacy equivalent - whatever you call homeopathy shops, I failed to look this up just for the sake of this post - delivers the appropriate remedies, 50 of which are homeopathic, 50 of which are placebo to a random selection of 100 of the patients.

See what happens.

Is there anything in this idea that you would object to? I'm a layperson with an interest in science, not a scientist. I remember someone somewhere saying that they wouldn't feel right giving some people the real stuff and some the fake, but that is the essence of a controlled trial, and the patients would know this going in.