Can you imagine trying to clean that up before you go home? That's insane. The bugs they would carry home gives me the shivers. They could carry home ticks, fleas, ants, and any number of different bugs. Yuck!
Sealed cell foam pads are a pretty good idea but a carpet will suck moisture out of the air and make for mighty cold sleeping arrangements. Moisture is the enemy which is why you air out your bed roll in the sun every day before moving on as a backpacker or before putting it back in your tent for the next night. It's the reason you strip out of your clothes before climbing into the sack. Your clothes absorb sweat and atmospheric moisture during the day and freeze you to death during the night no matter how much covers you use or how well your sleeping bag is rated.
Yeah, I am guessing it would be a moldy health risk pretty soon. Now if you owned a carpet factory and brought a new piece of carpet each trip or for every night it might make sense.