Does carpet deaden the sound too much?

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.

I think you're right.

Most recording studios don't have thick carpets and aren't heavily furnished either.

Give me an underdamped room rather than an oversampled one any day.

Everyone's room/ears are different.

Definitely a YMMV topic.

Damping/diffusion as needed. Just like cooking-salt/pepper to taste.