Am I missing something of is this really by design?
This is by design, and currently it is recommended practice. Once media set is erased, all information about the backup on this media set is erased as well, so backup to tape job have to place all data to tape from scratch.
Wich backupsheme's are you using?
General practice would be to have short retention for backup to disk and long retention for tape archives, because media storage is far cheaper than disk storage. For example: 2 weeks of disk backups and 1 month of tape backup seems to be most common retention.
Setup VEEAM with Backupexec allows this without any problem?
Could you elaborate this one, please?