Dedupe on linear media...
The biggest problem would be trying to dedupe against what is already on tape.
Say you did a weekly full backup and then daily differential and could fit several of these sets on a single LTO tape. To dedupe one full backup against the other and all the diffs you would need to reference all the previous backups - so either read them off the tape into disk before you start the dedupe/backup run which slows down your backup.
Tape is linear and will always be slower than disk or flash can be. Tape is good for archiving and long term backup. Tape is nice and portable. Tape offers large capacity.