Years ago I worked at a large company, and we purchased a SAN appliance to consolidate our storage. This was at a time when the majority of our servers used locally attached storage. This was a big purchase, and we knew that we had to plan for issues. So, we actually purchased two appliances and put one in our data center and the other in another building a few hundred meters away.
The idea here was to mirror changes from one box to the second, allowing us to easily recover systems in the event that the primary appliance had issues. There was a lot of work with vendors to get this working smoothly, and at some point, we were confident of being able to attach storage from either box to a server if one set of disks had issues. We had conversations about putting a third box in another city, just in case of a localized issue on our campus, but we weren't sure the the effort to restore servers in another location was worth the cost.
Recently I saw an announcement of a public preview of VM Restore Points in different regions in Azure. This allows you to take restore points from your VM, say in the US East region, and restore them in the US West region and bring up a VM there. While I don't know many disasters that could take out a region, there definitely could be a large outage with a major weather event.
This isn't automatic, at least not yet, but just the capability is amazing. To me, this is where a cloud provider shines over most organizations. The effort required to develop and maintain this technology is high and likely isn't feasible for most IT departments. However, in the cloud, it becomes viable at the scale of thousands of customers using this feature. While you hope you never need it, having it available might be handy for your peace of mind.