What we call the Temple Mount was really the Roman Fortress. The Wailing Wall is the remains of the Roman Fortress walls. Jesus prophesied that Jerusalem would be destroyed and that “not one stone here will be left on another; every one will be thrown down.” (Mark 13:2). The reason the stones around the Temple Mount were not thrown down is because that was the property of Rome where the Roman Legion lived.
Last stone thrown down? It ain’t over ‘til the fat lady sings.
Mark 13 specifically mentions the ‘buildings of the temple,’ and as I read things, a wall is not a building.