I just wanted to "show" that big vendors don't care about solving very practical issues: some companies still rely on backups on physical tapes, but the current versions of firmware of most libraries don't allow optimizing automatically the tapes. That's quite a problem when maybe a customer just bought 2,000 cartridges.
About the parallelism, it's quite simple: a tape needs to be read and optimized by a _tape drive_[0]. Libraries can be configured with a various number of drives, and the script manages all the available ones using the special device of the library and the `mtx` tool on Linux.
Also, you're right: it's impossible to decrease the optimization time of a single tape.[1][2][3]
Ah, while writing this, I noticed that HPE may have the appropriate tool on their autoloader.[4]
[0]: https://www.ibm.com/downloads/cas/3MD86RLJ
[1]: https://www.ibm.com/docs/en/ts4500-tape-library?topic=drives...
[2]: https://www.quantum.com/globalassets/products/tape-storage-n...
[3]: https://docs.oracle.com/en/storage/tape-storage/storagetek-s...