It also wasn’t an urgent problem as experiments like http were unlikely to reach broad usage due to critical failures like the one way links.
I mention this not to mock your “‘almost’ impossible” statement but to point out that you’re in good company
Here's a nice one with many public instances you can try: https://github.com/asciimoo/searx
I think this is one area where general purpose search engines are failing users currently. We should be able to tell Google "that one tweet from yesterday" and have it return something meaningful to us. Of course I understand that this is hard and becoming harder as social media companies hold on to their walled gardens, but clearly (to me anyway) the status quo is to the detriment of the user.
Anyway, for archival purposes you don't need to save the plethora of formats Youtube keeps at hand for each video, you just need one size in one codec, and it probably doesn't have to be 4K or 8K, which probably reduces the storage requirements by one order of magnitude or so.
edit: for example the average net worth of an American is 76,000$ but toss a couple billionaires in the mix, whose net worth is larger by such an enormous factor, that the "average" is misleading
(Of course, boiling a wide distribution of values down to a single value, no matter by which process, is fraught with problems.)
It's only 45 years of video per day. That is very, very possible to save. That's roughly 600 terabytes of storage space a day. Which means that per month you're generating a long term storage bill that is about $18k more per month.
So after a decade of operation your monthly bill is about $2.1m which is far, far, far cheaper than what we spend on plenty of things. Like I said above: This is not impossible. In fact, I bet the NSA is probably already doing it. At least for public videos. This truly is peanuts.