FWIW, I’ve been doing some improvised acoustic treatment of a dry walled metal shed workspace with a plywood floor and the introduction of area rugs has made at least as dramatic effect on taming overall echo and bothersome high-and-mid frequency “stridency” as has all the wall treatment I’ve done. So my take is, yeah,…I could see where carpeting has potentially a big effect and possibly an overly big effect on sound deadening within a given situation.
