What I don't get about homeopathy is that there's not even a plausible mechanism for it to work. So research into its effectiveness is like studying how well rocks repel tigers[1]. It seems necessary to show that a homeopathic "medicine" is substantially different than plain old water first. [1] https://m.youtube.com/watch?v=4GzMizVAl-0&pp=ygUTc2ltcHNvbnM...
You're right that no further study is needed for homeopathy, it simply cannot work at these kinds of dilutions.