Despite all the posts about the declining quality of Google, we haven't seen any serious competitors arise over the last years. DDG is at about 2% market share, which is great but still very low.
Apart from Google's monopoly and the big technical challenges, what would a competitor need to defy Google?
I think there is massive opportunity for domain specific search engines though, imagine a search engine specifically designed for software engineers and developers, or one for academic research (not just papers but all online scientific content, news and discussion), or one targeting the arts. I think it’s these verticals that could be incredible.
You then potentially move towards a building “meta” search engines (if your are older than about 35 you will remember these) that work out what you are searching for and uses a domain specific engine.
Edit:
Just to add to this, people who say that “decentralised” search engines are the only way to compete with Google are not completely wrong, it’s just that it’s not about protocols and distributed indexes. It’s about a community of smaller search engines working within specific domains and collaborating (commercially) on meta search engines, prompting people to search on each others engines if it would be better for that search.
We almost need an “Open Search Co-Op” which smaller search engines can join to share technology and refers users to each other.