This happens pretty frequently with single signals, so we know what that looks like.
An unattended broken signal gets treated like a stop sign (by law), and this immediately blocks traffic. It's a total disaster.
If it happens anywhere near a population center, a human will be dispatched to cover for the broken signal and dysfunctional law by manually directing traffic, and this gets you almost all the way back to normal.
If every signal failed at once, that would cause much bigger problems, but in the event that we know we're unable to repair the signals, which is the case here, we wouldn't just try to muddle through using the existing roads and systems. We'd define new systems that worked better in the absence of traffic lights.