You go way too far - the leap you have made from some sort of AGI to "now individuals don't have the ability to fully reason on their own" is not clear to me at all.

If people are spending less time bent over monitors or at desks under the dictates of corporate imperative, they will probably be spending more time doing actually interesting things. Reasoning is innately human. What we call "knowledge work" is not and is often anything but. People who are naturally curious will still discover things, even if irrelevant (from a market perspective) when the AI is on, for their own satisfaction.

If such an event were to occur, they would be called upon. It's really little different from what would happen today if suddenly the power grid or supply lines were down for a sustained period of time.