(IMO) Unfortunately, this is a space that can no longer be challenged. It would take a major corporation to attempt to build the engine and infrastructure to compete with Google; and they've tried. Microsoft attempted this with Bing and to a certain extent, they've been successful, but Google still reigns supreme.
What I would like is a search engine I can run on my own servers; tell it the domain of my site(s) and have it index them for me.
The companies in this space also fail IMO
Algolia.com (currently using) is super fast, but requires me to sync the json to their servers programmatically, nor is it self hosted.
Elastic.co (previously used) allows me to self host, but again, I must provide the inputs. It was also cumbersome to configure and maintain.
Search is very difficult to get right and people get frustrated when they can't find what they need.