[nodamage]

I don't know if OP changed their link but the one currently in their post (https://pubmed.ncbi.nlm.nih.gov/37232330/) did find DXM to be effective:

"Using objective and subject assessment tools validated in pediatric populations, this study provided evidence of the antitussive efficacy of DXM in children, aged 6–11 years, at the current OTC monograph dose and labeled indication. Compared with placebo, DXM treatment reduced cough rates 21.0% over 24 h (primary endpoint) and 25.5% during daytime/awake hours. In addition, children treated with DXM reported greater reductions in cough severity and frequency in the mornings and afternoons over 3 days than children treated with placebo. These treatment effects were statistically significant despite the study not reaching its planned sample size and are medically relevant."

Also as I mentioned in another comment, the author of original article misrepresents the findings of their own citation. DXM was found to be effective in adults, just not children.