Analogies aside, I’m not against anyone using Youtube (or any other platform) for distribution - just that it absolutely should not be also used for your actual archive. There are much, much safer and better systems for that.
Replicate to preserve!
The idea is that the "stuff" is archived or stored properly which is much less of a burden. When it's desirable to do so public displays of it can be created.
What is prohibited by law is distribution of copyrighted works. You need permission or an appropriate license from the rightsholders concerned to distribute or otherwise perform a copyrighted work in public.
It is nearly always the latter that a lot of these so-called "archives" trip over. Everyone, including Big Corp, is fine with having their copyrighted works preserved.
Obligatory IANAL.
The idea that museums should have exhibitions and be open to the public was a later development.