Here's an idea... what if search became a peer-to-peer standardized protocol that is part of the stack to complement DNS? E.g. instead of using DNS as the primary entry point, you use a different protocol at that level to do "distributed search". DNS would still play a role too, but if "search" was a core protocol, the entry point for most people would be different.
Similar to some of the concepts of "Linked Data", maybe - https://en.wikipedia.org/wiki/Linked_data.
The problem is getting to a standard, it would essentially need to be federated search so a standard would have to be established (de facto most likely).
Also, indexes and storage, distribution of processing load.. peer-to-peer search is already a thing, but it doesn't seem to be a core function of the Internet.
This is basically the same concept as making an "open" version of something that is "closed" in order to compete, I guess.