As Bert said, RAID is for availability and/or performance, backup is for disaster recovery. Backup (and snapshots) also help against accidental data loss by accident or mistake, which RAID does not.
Backup and RAID simply are not on the same spectrum. With modern file systems like ZFS, the areas are somewhat overlapping, but backup is still required.
Before we set up a server, we should evaluate the importance of the data protection, the required performance and the cost of potential downtime. This gives us the frame to plan the RAID level and so on.
Now RAIDs 1 and up can prevent unwanted downtime. As OP says, any rebuild poses some risk of finding another failed disk. But with the RAID running degraded, we have the time to plan ahead: Make plan A and plan B, assign a downtime, prepare the replacement parts, check if the backup is current and so on. Maybe we can test-run the procedure on our identical training server / organ donor. You have one, right? Because it is important.
And data is important, so we must act carefully and precisely. RAID buys us the time to prepare. It is even possible to just buy a new server and migrate next weekend without risking the rebuild.
In my case, with about 50 Petabyte disk space backed up to a centralized tape systems, disaster recovery can take several days. The incremental backup runs about 12 hours against the 50M files.
RAID 10 in this case protects against downtime, and the data loss between last backup and current status. But usually I try to replace the server before the disks reach critical age.
RAID allows us to act professionally, not react hurriedly.
