The odd thing about homeopathy is that is regularly outperforms placebos and in many cases even real medicine. Sounds like nonsense, but it shows that convalescence is more complicated than just the medicine itself. Many "traditional" doctors have little time for patients and basically just handle them as "take this and come back next week if it did not get better". On the other hand homeopathic "doctors" listen to their patients and talk about what the issue is. The result is that many minor issues are resolved basically without taking any medicine.
As anecdotal evidence, my wife had really bad back problems. No doctor could (or would) help her and she took relatively hard pain medicine. She went to a alternative practitioner that talked to her and gave her homeopathy and the issue resolved itself within a week. This was the first "doctor" to actually listen to her. If you think about it, it sounds like utter nonsense and that a psychiatry would be the better address than the orthopedy. But this is common place and in many cases you just do not need medicine. Most of the medicine you get is feel good medicine, like painkillers and few cases they are even counterproductive.
The important thing is that you need a doctor that knows the point where you need to switch to "hard medicine". In France for example, you need a medical degree to give medical advice and thus all homeopathic doctors have traditional medical training. Although I don't know how much they actually believe in the underlying idea, but the good thing is they will prescribe antibiotics where needed.
I think you can't dismiss homeopathy directly, for many it works. The real important thing that classical medicine must learn from it. Here and there there is interesting research into the placebo and nocebo effects. Doctors could learn to listen more to their patients and in some cases prescribing a placebo may actually help the patient.