> Sure, there are some high-priority bugs that are breaking the site that need to be fixed ASAP

This is why after making "deploy" a one-click operation, "roll back to the last deployed version" should also be a one-click operation.

Fixing things "ASAP" in a panic doesn't work at all well. First get to a known good state and then do a calm assessment of the right fix, taking as much or as little time as you need (and no need to work late).

I know that this doesn't work for all failures - If a server's drive fails, you still need a plan for how to repair - but it does for many common things.