The only way I can imagine this working is by twisting the definition of the words "search engine" enough that you can claim that there aren't search engines, but really there are still, just under a different name.

Search engines aren't actually the "problem" that OP is wanting to address, here, though. He just doesn't like the specific search engines that actually exist right now. What he should really be asking is how a search engine could be implemented that doesn't have the particular flaws that he's bothered by.