Let’s say ads will always make more money (I have no reason to believe they won’t), and that’s required to be the dominant search engine because the web is big and expensive to organize.

I’d bet there’s some way to characterize what I and others liked about the earlier web and create a search engine that just worries about that stuff. I’d pay $9/mo for whatever 1/3 of Google’s spend per user would get me. That’s not to say this thing would “beat” Google, but it could profitably exist.