A tripod is inherently more stable than 4 legs.Not true........try sitting on a 3 legged stool?
Four legs is generally accepted for stability in chairs.......but in office chairs on castors.......even 4 castors is not sufficient for stability with 5 castors being mandated for safety in the workplace.
The reason 3 supports is often used for turntables......is that the 3 supports will ALWAYS make contact on the supporting structure.
With 4 supports......depending on the load of the turntable.....only 3 may be making full contact.
With 4 legged chairs......a person's weight will 'spread' the bottom of the legs so that all 4 legs are weight-bearing whilst without the load of an occupant......only 3 legs may be fully in contact with the ground?