Absolutely! You're preaching to the choir here.
However, that said, over ~3 decades I've found that having a successful rsync exit code and alerting when that is not true, along with periodic "full" rsync checksum runs, is effectively a failsafe way of ensuing a good backup.
For our less critical systems, this plus "spot checking" by regularly going in and looking at "what did this file look like a few weeks ago" (something we commonly use backups for), has proven pretty effective while also being low work.
For critical systems, definitely do test recoveries. Our database server, for example, every week recovers the production database into our staging and dev environments, so backup problems tend to get noticed pretty quickly.