What if the site is simply gone, or now belongs to someone else who is not the owner of the archived content?
https://www.joshualowcock.com/guide/how-to-delete-your-site-...
You'll need to prove that you are the owner of the archived content, or were the owner of the domain.
It's a discussion that's been had for literally decades, because most tech-fluent people realized a long time ago how a copyright that's designed for physical distribution does not lend itself well to the intangible nature of the web, were replication is trivial and in many cases a mandatory necessity to enable a lot of functions in the very first place.
Sadly that discussion simply died out at some point, I think it was around 2010 when smartphones and social media started to boom, so the copyright reform that was supposed to "fix" all this never came.