I suspect that when they hired Pace there was a strong suggestion that he take Fox. And he was saddled with Cutler. So Nagy didn't really get his QB until 2017 and didn't get his coach until 2018. It made sense to extend Pace to 2022 and have him and Nagy paired together.
Plus he inherited a pile of shit, and everybody knew it. Fangio said "this defense isn't built for anything". Granted 2017 was basically a lost year, and Pace should have fired (or should have been able to fire) Fox to bring in his HC/QB at the same time.