Gregory's Server@fatsam “planes would have fallen” is an exaggeration. It was likely that ATC systems would have crashed, so planes would have had to divert to the nearest airport. If that was expected to happen, none would have taken off.
I agree with your wider point though.
@bernardlyons if you're going to put quote marks around something responding to me, at least use my actual text. Might and would are not the same.
Most commercial flights were grounded on New Year's Eve 1999. I'll leave the rest to people who worked on those systems.