ping
They don't have suitable material (carbon nanotubes would have to be meticulously made).
The technology will be useful whether a space elevator from earth surface is ever built or not. Cables of tensile ultra-strength will allow construction that is impossible now.
The weight of the supporting cable would drag the whole mess back to earth, unless an elaborate counter-weight system were devised to anchor the cable far *beyond* GSO. It would never work.
The lower the orbit the faster the mass must move to sustain orbit. The lower sections of cable would be moving *far* too slow and a staggering gravitational force would pull those sections of cable downward toward earth. A counter weight much farther out from GSO is the only way to counter that force, but the cable would be ridiculously long and not have the tensile strength to handle the forces.