WebArchive link is hidden so deep in the "About the source" page that vast majority of Google users won't even know that it exists.
There is excellent browser extension called Web Archives[0] that hooks all major web archiving services e.g. Archive.is, Wayback Machine and others in one place.
Click a result's three dots menu. Underneath all the main call to action buttons (Visit, share, save) is a Wikipedia description of the site. Underneath that is a "More about this page" button. On this separate page is a description of the company, social media links, reviews, generic results for the company, and, finally, some 1100px down, "See previous versions on Internet Archive's Wayback Machine" in a 14px font: https://imgur.com/a/IMgVDpV
What's the ETA for this being removed due to lack of use...
Give a man a hypothetical infinite amount of meals and he will poison the village well so there will never be fishing again.
Non-disclosure agreement
Google likes to influence search results, hiding ones it doesn't like, and elevating those that the Company supports. Wayback Machine has been very reliable so far, I hope it stays that way.
(There are some tiny subsets which are rudimentarily full-text searchable; and some efforts to make domains findable. But nothing remotely like even Google 1.0 mapping URIs to organic terms.)
And no, the IA is already not an impartial archive: https://archive.org/post/1126216/kiwi-farms-removed-from-way...
There is also the matter what IA will be able to archive. The the machine learning gold rush more and more site operators see dollar bills in front of them and are restricting who can crawl their content. Google is in a special position here because almost no one can affort not to be crawled by Google which is what made their cache especially valuable in addition to the IA.
Hopefully they are also making substantial donations to the Internet Archive, since they will be directing a lot of traffic into it and basically using their infrastructure as a feature on their main product...
EDIT:
Apparently they are collaborating but there are not much details [0]
[0] https://blog.archive.org/2024/09/11/new-feature-alert-access...