While something like Kagi is nice, at best they can become a bespoke and expensive, and maybe excellent as well, suit maker on an experience stretch of a very expensive city. I don’t think general search is that.
It seems to me that there are always spaces in a market for companies that aren't necessarily looking for world domination in a segment, but just want a sustainable business which does their thing pretty well. ie - Kagi doesn't have to be The Google Killer, it just has to work well enough that people like me give them money and like what they get in return.
Kagi became profitable in 2024 after 2 years of business, and that's even with the (probably considerable?) (current) costs of using Google's index. If they carry on being a niche business, but one that continues to grow (currently 41k members [0]) then that works nicely for me, and presumably lots of other people like me. They don't have to be "general search", they just have to be good enough that people pay for it.
Yes, this is what constitutes between 99% and 100% of the world economy.
There’s been dozens of attempts at this that have all failed because there’s no real market demand for it. “Open source” is not a feature in most cases.
What exactly would this do that is an unmet need of enough users to make it worthwhile?
I think it’s definitely seen as one by people who understand it and what it can prevent. Similar to how many people don’t seem to care (or rather don’t think) about privacy until it dawns on them once a lack of privacy bites them.
But you are right that it’s not really a marketable feature for a wide audience.