It all depends on the venue and the type of kit. If it is a small venue which does not have an established drum riser in it, you are correct, you will see it placed on carpet so the kick will not slide, since most stages are made from some type of plywood.
In bigger venues, which have permanent drum risers installed, you will not find carpet, but instead small hooks in the riser to act in the same capacity, however, in these styles of venues, you will also find that the kit is not as miced as much because the carpeted riser does dull the sound, which means you need to mic it more.
In even larger venues (1000+ capacity), you will normally find the kits installed behind a case of plexiglass, then each piece of the kit miced and run through an individual channel on the board. This created a more pure sound for the audience without any vibration distortion.