It's probably better for the user to search the original URL themselves on the Wayback Machine. If you cite with a Wayback Machine link when the original link still works, you're just creating needless work for a non-profit. An archive isn't a CDN.
> or at least creating
I agree on creating.
Do you also expect universities to have an archived version of every article and book their professors cite?
Relying entirely on a single nonprofit (archive.org) to provide a honest snapshot of every cited link, at the time of citation, sounds much more unreasonable.
Yes. Libraries should be able to back-reference every citation that is included in every paper that they publish, and so should the journals. That is paramount to the scientific method. Anything that you have not verified yourself should have a clear citation that you're able to prove.
this could then be stored on a university server for future reference.