My understanding is that it would be under tension and orbiting at beyond escape velocity, such that if it got cut off, it would fly away from Earth. Still bad, but not catastrophically. Maybe we could even recover it.
That all assumes that it got loose at the base and not part way up within the atmosphere. If 9/11 can happen, this can happen. All that cable and kinetic energy has to go somewhere.
If your bad guys can get high enough to sever your cable, they can get high enough to do a kinetic or powered bombardment and cause magnitudes more damage.
Plus accidents are more likely than you think. A rocket just exploded this morning, and read up on rates of railroad or shipping screwups. A train full of apples and pallets of kleenex going over ain't a big deal but the same containers falling out of the sky will certainly cause more damage.
I can’t take a tube of toothpaste on a plane. How am I going to pack a bomb large enough to cause that much damage. Why don’t people blow up planes with that method today?
If a tether breaks high up, then only a few kilometers of the tether hit the ground. Anything higher burns up on the way down (since it is very thin, so surface plasma heating doesn't take long to destroy it)
