Nah, it wouldn’t do much damage. The tether’s whole job is to be strong, but light. And being a long, thin fiber, it’ll have a pretty low mass to surface area ratio (high drag in atmo). If it did come down, it would likely mostly burn up, or mostly be slowed down by the atmosphere.

Additionally, the length of tether with the most tension on it will be the section nearest to the ground. If the tether snaps near the ground, the whole thing gets hauled up to orbit for good.

To be clear, I’m actually not in favor of space elevators in general, I think there are many much more practical ways to get to orbit. I’m just saying that a broken tether should not be the end of the world.

If you really want to build something like a space elevator though, you should check out the tethered ring concept: youtu.be/8B2iqiKehyM?si=9IM8FU-uI7CIoPtX