Actually, the reverse is the case. If the entire internet was filled with only "positive-quality sites", there won't be need for a search engine.

The work of a search engine is to wade through the internet and find the positive-quality sites itself.

You're forgetting the other half of the search engine's job, which is to find sites that match your search. Back when Google first came online, they were head and shoulders above Yahoo!, Altavista, and whatever other search engines existed at the time that I've forgotten. Because their indexing actually did a good job of spotting keywords, and returning relevant results. And this was back when the Internet was filled with positive-quality sites. Many of them were amateurish Geocities pages, but that was head and shoulders above the AI slop that the search engines these days have to somehow detect and filter out.

So even when the Internet used to have a much higher ratio of positive-quality sites, a search engine was still necessary, and so much faster than finding new sites yourself.