> Most studies have found that dextromethorphan performs the same as a placebo
The citation linked does not support this claim. In fact it suggests the opposite:
"Dextromethorphan was tested in three of the included studies (Lee 2000; Parvez 1996; Pavesi 2001). One report on a series of three successive studies on a total of 451 adults favoured dextromethorphan 30 mg given in a single dose to placebo in terms of cough counts (measured through cough acoustic signals using a microphone on the nose) and subjective visual analogue scales (Parvez 1996). Differences in mean changes of cough counts between active treatment and placebo varied from 19% to 36% (P value A study involving 44 participants tested a single 30 mg dose of dextromethorphan versus placebo (Lee 2000). Both treatment groups showed a decline in cough frequency (from 50 to 19 per 10‐minute period in the active treatment arm compared with 42 to 20.5 in the placebo arm, P value = 0.38 at 180 minutes follow‐up). Mean subjective cough scores showed a decline from 2.0 to 1.0 in the active treatment group compared to a decline from 2.0 to 1.5 in the placebo group (mean difference in decline in cough scores 0.5 at 180 minutes, P value = 0.08).
Pavesi and colleagues also tested a single 30 mg dose of dextromethorphan versus placebo (Pavesi 2001). Outcomes were measured through a three‐hour continuous cough recording, measuring cough bouts, cough components, cough effort, cough intensity and cough latency. Average treatment difference was 12% to 17% in favour of dextromethorphan for cough bouts (P value = 0.004), cough components (P value = 0.003) and cough effort (P value = 0.001), with an increase in cough latency (P value = 0.002)."
Two out of the three studies found DXM was effective in adults. The studies did not find the same efficacy in children but that could be due to differences in dosage (adult dosage is 30mg, child doses vary based on body weight) or in measurement techniques (as far as I can tell the child studies measured results via parental survey as opposed to more objective techniques like cough recordings).