They do have redundant backups: enough spare capacity exists in the other centers to carry the load the Chicago center dropped. Switchover to operations at alternate facilities was accomplished (and reversed) without incident. Yes, it took some time and there were substantial flight delays, but this is a once-in-a-great-while type of failure.
Or are you talking about backups so expansive that in the event of a problem, no one need ever know anything ever happened, whether we're talking about the failure of a single chip or the destruction of an entire facility? I agree it could be done, but at what cost? As a taxpayer and occasional traveler, I'm satisfied with the level of redundancy they have now.