Sorry the idea of continuity holds - but its not quite the same as banking cutover to a standby data center. A data center cutover is automated with redundant copies of the databases held at secondary sites. The system does a cut over then rollback out of the last few minutes then rollback forward and reapplies transactions and the users may get an initial issue at ATMs and online but normally only seconds. In a disaster recovery the system is far more extended and the business can afford an hour down while the recovery service comes in. Everyone is called out and everyone works to their script. The systems are designed to failover to the backups and indeed with all the fault tolerant machines I worked with the user doesn't notice any part of the system being crashed.
In the aircraft case the pilots have to pick up the aircraft in seconds and get it right first time without any external support. The system is actually
designed to failover to the pilots. It is not a backup system or a remote FMS that picks up the pieces it is the flight crew. The crew are actually seen as the backup to the FMS and Autopilot. So to go back to your business analogy its as if the failover all works but nobody is bothering to keep the backup system updated or running and they've saved money by not paying a disaster recovery service.
This is not fair on the flight crews - they can be put into a position that they have sketchy knowledge of and zero practiced skill. As you roll fast inverted in the incipient spin with a dead engine on the inside is not the time to start learning how to do a spin recovery in that aircraft type IMC on limited standby panel.
