I rarely visit sites out of a band of 15 or so, and I only use Google to find pages within those sites (which itself follows a normal distribution). I.e. I know I want a page from stackoverflow, or Wikipedia, or arxiv, or Reddit, or Yelp but rather than navigating to those sites I just cmd+T in Chrome, type keywords, and scroll to the site's link on the result page which is almost always at the top anyways.
I'm sure others use Google like this too (varying on your culture's go-to sites), so does it even need to exist as it does right now? I could imagine a new app that indexes just within this band of sites. And Google or some other app is relegated to "the rest" for rare occasions.