It is not just we who forget. When archaeologists dig up a site in Mesopotamia there is a good chance some cuneiform material will be exposed — inscriptions, clay tablets, seals and so on. From these we get to know a lot about people we can never meet and can piece together elements of our own history which otherwise go unknown. But in places such as central Turkey and the Indus valley there is evidence of civilizations which do not appear to have had any form of writing. Much can be inferred from architecture and artifacts but, in the end, we know little about how these peoples thought and felt, what they found important and what they did or did not know. When the electricity fails, streaming moves us from the vocal to the silent, from the literate to the illiterate from historical facts to mythical guesswork. At the moment we have a rich mixture; but give it a century or two and how much will be left for some future generation of interplanetary travellers piecing together the evolution of the universe from the remains of a depopulated earth? Does it matter? If what you are streaming matters, it matters.
I went to a very interesting British Computer Society lecture about 20 years ago entitled "Keeping Digital Data Forever". It's a problem on multiple levels.
Access to old media readers (e.g 5" floppy drives, DAT tapes) gets harder over time.
Physical media can degrade. Magnetic media can demagnetise, the plastic substrate of CDs breaks up.
Older encoding formats could be lost.
One example given was the electronic Domesday book from the 1980s. This was meant to be the digital equivalent of the original from 1086, a thousand years later, but it used 12" laserdiscs and the storage format was proprietary. Digital Domesday Book lasts 15 years not 1000
A lot of backed up data nowadays is encrypted and, obviously, the encryption keys are not usually stored with the media.
If we manage not to blow ourselves up or send civilisation back to the stone age, then 100 years in the future computing power may well have advanced to the point where decryption of this is trivial but if not, it's going to be lost forever.
Data is becoming increasingly ephemeral. Everything has to be immediate. People just don't think of what might happen even 10 years in the future and simply don't want to think about 50-100, i.e when they're dead.