I was recently did the same thing. I had about 2 old OnStream 30 GiG tapes and a hand full of old QIC-80's. Not even mention the CD-R pile in my room.
During the years I never had the space to just extract everything and sort though it all. Not to mention I would move backup data from tape, to CD, back to tape so I have copy's of the same things all over the spectrum. I have recently started consolidating it all, finding an old OnStream tape drive and old QIC floppy drives to restore everything to a single drive, get rid of all the duplicates and save the important stuff on archived DVD media and/or "the cloud" It was a nightmare but now I don't have to worry about trying to get hold of a bankrupt tape drive company's hardware in another 10 years.
I will then delete the tapes and burn them.
If it was hand labeled by a professor he liked or someone famous like Bill Gates I could see that. But there is no other reason to keep it around once it's contents have been properly indexed and stored. The only exception is when you need the obsolete media to be used in another obsolete computer. AKA making a disk for a cC64.
Let me put it this way. What do you think will happen in 10 years, when someone else finds that box of media. Even if he was told that it was all indexed and stored, he might question it and do it all over again "just to be sure"