There's a couple different threads here.

Can we make a decentralized search engine. Which breaks down into two questions, is it technically feasible and is it socially feasible?

(Maybe the word search would be a bit more broad than retrieving web pages. It could be for everything right.)

I don't know but I'm inclined to say that the difficulty will be more on the social side than on the technical side.

The web was very decentralized 20 years ago, and we had all manner of peer to peer systems already. There just doesn't seem to be much appetite for that kind of thing, at least in the mainstream.

Although there might be something to it, with the AI part of the equation.

Like we had self hostable services for a long time, most people just don't want to be a sysadmin.

Well, I gave Claude root on my $3 VPS. Claude is my sysadmin now. I don't have to configure anything anymore. Life is good :)