> Ultimately I think it’s because the internet is just too big!
I would disagree actually. I think the majority of searches people do and the solutions they would be satisfied with require only indexing major sites. Create a better UX attached to PageRank of the top 10-100k+ Alexa ranked sites and you'd have a competitor that could focus on other improvements.
At the bottom you could search Google or DDG if you want more niche results.
I.e., optimizing UX of the p90 searches would be enough for people to move and the p90 of searches are happy with a pretty narrow range of sites. (You could insert value prop of: no ads, no tracking, and crowd-sourced refinement -- i.e., realtime upvote/downvoting -- of the top results, previews, caching, more knowledge graph stuff on the right side, deeper metadata processing of top sites (i.e., avoiding the need to 'site:*'), or some other revolutionary UX like a one sentence hypothesis solution of exactly what the person is asking for again upvoted/downvoted for refinement -- Google does this but there is a lot of room for improvement). It's fun to think about. There is an order of magnitude in both precision and accuracy that can be improved for huge swaths of common questions people ask on Google.