FileVault’s full disk encryption is a really nice feature of macOS, and making a bootable full-disk daily backup of your Mac’s internal hard disk or SSD using Carbon Copy Cloner or SuperDuper! is a great way to avoid downtime if your internal hard disk dies. You just reboot from the backup drive and get back to work, having lost at most 1 day of work.
However, you may encounter trouble when trying to create an encrypted bootable volume on your external backup drive. I had no trouble finding helpful articles to tell me how to reformat the external drive as encrypted, or even to convert the disk non-destructively to an encrypted volume, but none of them actually worked. In every case, the UI was happy to say it was gonna encrypt the drive and even gave me a recovery code and took a passphrase for the encryption, but then failed with the following message:
Unable to create Core Storage Logical Volume Group.