One way to replace search is to return to curation by trusted parties. Rather than anyone putting a web page up and then a passive crawler finding it and telling everyone about it, (why should I trust any search engine crawler,) we could "load" our search engine with lists of websites. These lists are published and maintained by curators that we have explicitly chosen to trust. When we type into the search box it can only return results from sites present on our personal lists.

e.g. someone's list of installed lists might look like:

- New York Public Library reference list

- Good Housekeeping list of consumer goods

- YCombinator list of tech news

- California education system approved sources

- Joe Internet's surprisingly popular list of JavaScript news and resources

How do you find out about these lists and add them? Word of mouth and advertising the old fashioned way. Marketplaces created specifically to be "curators of curators". Premium payments for things like Amazing Black Friday Deals 2019 which, if you liked, you'll buy again in 2020 and tell your friends.

There are two points to this. First, new websites only enter your search graph when you make a trust decision about a curator - trust you can revoke or redistribute whenever you want. Second, your list-of-lists serves as an overview of your own biases. You can't read conspiracy theory websites without first trusting "Insane Jake's Real Truth the Govt Won't Tell You". Which is your call to make! But at least you made a call rather than some outrage optimizing algorithm making it for you.

I guess this would start as a browser plugin. If there's interest let's build it FOSS.

Edit: Or maybe it starts as a layer on top of an existing search engine. Are you hiring, DDG? :P