I don't support the use of homeopathy, but I don't think that's a great analogy. Polygraphs are used as an interrogation technique, where psychological tricks and deception on the part of law enforcement are "fair game" (we could enter a long discussion as to whether or not deception during interrogations/interviews should be permitted, but regardless, that's the status quo right now).
Trickery and deception when it comes to medicine and personal health are never fair game. I think there's definitely a difference between police telling a suspect "we know you did it" (when they don't actually know) and a doctor telling a patient "take this and you'll feel better" (when the drug actually does nothing).
Also, polygraphs are a little bit more functional than homeopathic medicine: a polygraph can not only induce nervousness, but can also notice it in some cases (even if the nervousness may not be concerned around a particular question and may not necessarily indicate deception and even if there are false positives). This helps create a feedback loop which makes it more powerful than a pure placebo (e.g. a "lie detector machine" you hook someone up to which isn't powered on at all and does literally nothing).
It's been shown that telling someone you're giving them a placebo can still bring benefit, in which case I'm okay with it. But giving someone a placebo or homeopathy pill (same thing) and failing to disclose it contains no active ingredient is pure deception, unless the patient has given consent that they may receive a placebo, like if they're in an experimental trial. Even if someone does show improvement after receiving the placebo, it's never justifiable to outright lie to them.
Trickery and deception when it comes to medicine and personal health are never fair game. I think there's definitely a difference between police telling a suspect "we know you did it" (when they don't actually know) and a doctor telling a patient "take this and you'll feel better" (when the drug actually does nothing).
Also, polygraphs are a little bit more functional than homeopathic medicine: a polygraph can not only induce nervousness, but can also notice it in some cases (even if the nervousness may not be concerned around a particular question and may not necessarily indicate deception and even if there are false positives). This helps create a feedback loop which makes it more powerful than a pure placebo (e.g. a "lie detector machine" you hook someone up to which isn't powered on at all and does literally nothing).