That it doesn't work chemically is not a value judgement though and complementary medicine is beneficial for psychological reasons, the placebo effect is nothing to be scoffed at. People only get worked up about homoeopathy because sadly the homoeopathy industry is more interested in ripping you off than the pharmaceutical industry who are greedy gits in their own right. If homoeopathy was appropriately priced for what it is it would probably draw a lot less criticism. That said humans also associate cost with greater potency/quality you can price two identical steaks differently and most people will say the more expensive one tastes better so perhaps the price in some way helps enhance the placebo effect and we can find justification in the pricing that way.
Completely agree apart from the value judgement bit, working chemically is the only quantifiable measure we have. a homeopathic remedy may a positive difference to an individual patient with the correct mindset, but an antibiotic course will kill bacteria in a patient whether they believe it works or not.
I'm happy for people to take whatever they please, you pay your money and take your choice.
I dislike the the term "alternative/complementary medicine" though. For me it implies equality with existing "medicine" treatment.