Thanks for the response, I appreciate it. I think we're on the same page, regarding a "real" failure, and you raised an interesting point, regarding a misconfig. Our scenario is slightly different than the one you described (we have/use only one "Backup to Tape" job), but there are similarities:
We run four "Backup Jobs" (to file) that back up four servers to the Default Backup Repository. The four jobs run sequentially and, then (upon completion of the fourth "Backup Job"), the "Backup to Tape" job runs, backing up the Default Backup Repository to tape. As you mentioned, though, "always continue..." and "eject media..." are selected ("export" is not). This scenario runs daily (Sun-Fri = incremental, Sat = full), and tapes are also changed daily (per media rotation strategy).
Could be I'm missing "the bigger picture" but, due to the sporadic occurrence of this issue on our end, I'm inclined to believe we may be running into either a timing issue between Veeam and the Tape Library (similar to that mentioned by the OP), or else a tape is getting physically stuck (ie. "real" failure). Unfortunately, I'm 2,000 miles away from the unit, so I'm unable to personally observe the unit's behavior or otherwise verify this theory, but I'm working with the device operator to try to determine that.
Regardless, your response and the one I received in my official support case are virtually identical, and you've both answered my question as to whether or not disabling the registry key will prevent a "red alert" in the event of a true hardware failure (that answer being "no."). As for how we're going to proceed from here, while we certainly appreciate having the option to disable the warning, we've decided to leave the registry key "as-is" (warnings enabled). When it comes to backups, especially with being new to Veeam, I'd prefer to err on the side of caution.
Thanks again for your response and assistance, Konstantin!
Support case: 02084013