That is a start, but I mean an actual inverted index, and preferably even more structured indices with appropriate metadata. Web servers should also be responsible for archiving themselves and providing a change history.

No, an actual search index, offerring word-to-URL mappings, along with metadata: creation and revision dates, authors, titles, file and/or MIME types, URLs within the text, other attributes, etc, from which a search interface could query.

Page-ranking would remain an issue, likely outside this scope.

I'd like to see some sort of cache-and-forward structure.

And you'd be relying on good-faith actors, which means heavily penalising bad actors.