If we were to design a brand new internet for today's world, can we develop it such a way that:
1- Finding information is trivial
2- You don't need services indexing billions of pages to find any relevant document
In our current internet, we need a big brother like Google or Bing to effectively find any relevant information in exchange for sharing with them our search history, browsing habits etc. Can we design a hypothetical alternate internet where search engines are not required?
Indexing isn't the source of problems. You can index in an objective manner. A new architecture for the web doesn't need to eliminate indexing.
Ranking is where it gets controversial. When you rank, you pick winners and losers. Hopefully based on some useful metric, but the devil is in the details on that.
The thing is, I don't think you can eliminate ranking. Whatever kind of site(s) you're seeking, you are starting with some information that identifies the set of sites that might be what you're looking for. That set might contain 10,000 sites, so you need a way to push the "best" ones to the top of the list.
Even if you go with a different model than keywords, you still need ranking. Suppose you create a browsable hierarchy of categories instead. Within each category, there are still going to be multiple sites.
So it seems to me the key issue isn't ranking and indexing, it's who controls the ranking and how it's defined. Any improved system is going to need an answer for how to do it.