The best they could do with fiber cuts is to segment the Internet geographically until the cuts were repaired... alternate routes would be partially successful in the interim, but the performance (congestion and latency) would generally be terrible.

Stupid BGP tricks would work in the short term, but china, iran, etc have already been doing that sort of thing for a while, and countermeasures have been worked out. The white hats know a bit about network engineering and the Internet, so it's not as if the world is defenseless against DS sabotage.