I've seen a lot of carpets in studio and live sessions. Sometimes there are on the floor and sometimes directly under guitar amp. What's their purpose?
Bare floors can cause extra reflection of sound, sometimes causing unwanted reverb or reinforcement of high frequencies. The carpets mute the reflective surface.
An amp sitting on a hard surface may produce some vibration between the feet and the surface, so a carpet can help with that. They also slide around more, so if you bump them they may skid, or in the case of tilt-back like the photo, fall over. Also, if the metal feet or corners have scratches in the metal, they can leave marks or scratches on unprotected wood floors.