"We" in the article refers to the collective of individual users, not search engine companies.

The spirit of the article is about how this can be achieved in a decentralized way without search engines, and instead with just your LLM and the embedding databases that it proposes that each website would publish.

A problem with this is that you still need to keep local copies of these databases that you get from crawling the web, and train your LLM to use it.

I don't think so. AFAIK when you do that, it searches normally based on the terms you give, and then does RAG on the results. Semantically this seems like "doing RAG on the web", but RAG is a specific operation that is only being applied to a subset of the web (indexed results) in that case.