Assuming ~35PB of content stored at YT, should cost roughly $70M for IA to buy the necessary storage infra and maintain it into the future (their costs are ~$2/GB for perpetual storage).
But what could those criteria be?
You can't just select out all those fast-talking "influencers" that shill and lie their way through hours worth of video just because they're shit, because sometimes those videos have thousands of people that DO like them, making them perhaps interesting to a sociologist 300 years from now.
2000-year old Roman shopping lists, personal letters and obscene graffiti are intensely interesting to historians now, but would have been worthless to their owners even a couple of days later.
That's really unlikely, given it's all just digital and electricity. Ignoring that our pseudo-global society will have collapsed long before that and ignoring that the digital era unlikely lasts that long ...
... assuming humanity actually keeps going as it is ...
... there is no way people in 300 years will be able to read any device from today. Hell, the CD-ROM is dying and that's young.
One of the most impressive things you can do is, try searching up a landmark. My personal favorite is the [Jumping Stone](https://www.youtube.com/watch?v=u1TtMN8nXTM) on the Nias Island of Indonesia. What would have otherwise just remained a novel tourist attraction, forgotten by the modernity of the 21st century, is now essentially a "tag" which has hours of footage associated with it. Thousands of tourists travelling back and forth, locals growing old, new people being born, buildings being built and demolished around it. You can even just study how video quality improved in that particular region. That there IS something wholly unique to this era and definitely worth preserving. YouTube as a company has figured the logistics of storing it, but the question of how humans can hope to read such data remains yet unanswered.
If the IA didn't exist, we'd have to invent it.
I suspect if the IA ever decides to properly archive YouTube, they'll interface with the folks that run it directly. Archive Team is, to put it as diplomatically as I can, not a good organization.
You know, a part of the original company vision for YouTube prior to the Google acquisition was really something akin to the IA, in that they did pride themselves with hosting footage of the Indian Ocean Earthquake:
https://www.youtube.com/results?search_query=Indian+Ocean+ea...
Now, acting as diplomatically as I possibly can, I can say that your suggestions of the IA and YouTube interfacing together were at a previous point in time a continuous process. But a number of factors have made direct cooperation between the IA and Google (thereby YouTube) come to a screeching halt.
At this current point in time, we stand at a historical crossroad. And I'm only here to just act as a humble messenger ;)
A couple of months ago, they sent me a thumb drive of some stuff I requested (for a nominal processing fee).
In my case it was some TV footage broadcast on the evening of September 10, 2001.
http://www.autonomoussystem.net/2013/07/youtube-slowness.htm...
I'm surprised by how magnetic storage continues to decline in price as densities continue to increase. I wonder where the end actually is.