Because the tendency to leap out of the way when someone else heads for the same chair as you is not what that game is about.

Y’all, there was a game of musical chairs at my work Christmas party that seemed likely to dissolve into bloodshed at any moment.  I was actually thrilled to be out in the third round — opera people will take your chair and leave no survivors.  Picture Game of Thrones (probably), but with girls in adorable scarves and murder in their eyes and a circle of plastic chairs.