If homeopathy worked consistently, provably, demonstably better than placebo then someone would have claimed the 1 million dollar prize offered by the well known sceptic John Randi and his foundation.
Also it contradicts the entire scientific edifice as we know it.
Do not underestimate the placebo effect. The placebo effect is based on the wonderous healing abilities of the human body.
There was a famous head of a drugs company recently who admitted that most drugs do not work any better than placebo in most patients. He was saying this advocating the use of genetic data to better target drugs to patients.