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:
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 ;)
You have to, however, also consider the multi-domainness of YouTube videos. Yeah sure, there's billions of hours of clips not one person can watch in a single life-time. But unlike your 2000-year old Roman shopping lists, we have footage of events that are anchored to a particular time-period. Or location.
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.
There was something of a brokered agreement between Archive Team/Twitter to upload a fraction of Tweets to the IA. That too, unfortunately, ceased some time last year. Either way you might want to take a look at https://archive.org/details/twitterstream
There was also a sister website called "Welcome to Republic City" which is now available on BlueMaxima's Flashpoint:
https://bluemaxima.org/flashpoint/