On one hand, we are building something like that using indexers that go out of their way to crawl homeservers and generate feeds.

On the other hand that is not a part of the core protocol so I try to make that distinction super clear.

We expect there will be different indexing for different apps and higher level protocols, and we don't expect that they will all interop, or that indexers can be censorship resistant... kinda impossible to make search censorship resistant, when it is hella expensive and thus only few will ever do it at a large scale.

The web is distributed, search engines are not, and probably never will be.