This scenario works by cognitive zombification.  First, we become reliant on determining direction via compute (reporting, logistics, operations, prediction).  Then, we willingly dedicate resources to displace human cognition from the process.  Stability would be something like the first Matrix movie, which I think is the true allegory of the first movie.  The real gray goo, powered by zombie resources and hope, is when knowledge eats itself, out of control, with zombies operating/maintaining.