I have to put. One on carpet as for some reason when it's on laminat/or on desk it seems to pick up dog hairs so I put it on a rug and it's perfectly fine no issues and it's year and half old.
If your PSU suck the air from under the cassig, then yes... It will cause issues, with dust and sometimes less air to be suckes in, which can also lead to thermal issues. The best way to overcome this issue is to mount the psu upside down. It will work as an exhaust and you can let your pc sit on the carpet no problem.
The PSU can overheat due to choking for airflow. Assuming your PSU is on the ground. Simple solution is to put a piece of 2x10 under your computer to keep it off the ground.