I think that how big those problems get is going to depend on how much critical infrastructure we can hack back into a working state despite the fact that it can't phone home, which is going to be a problem if nobody knows how to work offline anymore.

Or, if it's a political scenario, it may depend on how well we can coordinate en masse without the cut connection. If we can exceed a certain threshold then we'll have removed the incentive to cut it in the first place.