Does carpet deaden the sound too much?

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.

Whether we like it or not, and many do, the room is an inevitable part of the sound we experience.

I wonder if anyone has ever tried to play their system outdoors?

The closest I ever got was to lend mine for an engagement party set in very large hall, I'm guessing 25 metres long by 15 wide and maybe 7 high.  It was ok, if a little small sounding.

Domestic systems are basically small boxes operating within larger boxes.