like Kagi is doing
I haven't seen much to suggest Kagi's results are better than Google's. But that's as much a function of time and horsepower as anything.
I would argue that the private model is what's fundamentally wrong with modern search. Nationalize Google and make it a public utility, like any public library or publicly financed research institution. Open up the front end source code and let people apply their own filters and modifications, rather than locking everything down to force feed you sponsored content.
That's the only real way to fix search.