That might be fine for a single or a few planes. But given the magnitude of the outage, what if a single airport had dozens of planes landing anyway.

There's a very good reason airport traffic control exists.

I'd be highly surprised if ATC systems were affected by this, but if anyone wants to correct me please do.

I wouldn't expect emergency rooms and 911 to stop working either, but here we are, so until someone says otherwise, I'm assuming some ATCs went down too.

I imagine the flight planning software they use was affected (so their ability to coordinate with other airport's ATC), but not their radio systems or aircraft radar (nearly all radar systems I've worked with are run on Linux, and are hardened to the Nth degree). Been out of the game for 12 years though, so things have likely changed.

The Tenerife disaster (second-deadliest aviation incident in history, after 9/11) was ultimately caused by chaotic conditions due to too many airplanes having to be diverted and land at an alternate airport that wasn't equipped to handle them comfortably.

I'd argue that Tenerife was due to taking off (in bad weather), not landing. But of course, a bunch of planes landing at the same airport without ATC sounds quite dangerous.

There were a lot of contributing causes, but it wouldn't have happened if not for the fact that Tenerife North airport was massively overcrowded due to Gran Canaria airport being suddenly closed (for unrelated reasons) and flights forced to divert.

The issue wasn't with landing specifically; I'm just using it as a general example of issues caused by havoc situations in aviation.

Also lack of visibility. The two pilots couldn't see each other through the fog.

Pilots know where there are other places to land, e.g. there are a lot of military strips and private airfields where some craft can land, depending on size.