Any Google killer needs to have search indexing technology and infrastructure as a core competency to be truly successful. Kagi has done a great job of solving some of the UX and privacy problems endemic in online search these days, but at the end of the day they could be snuffed out at the whim of the big search providers (Google, Bing) if they decide to kick them off until they can get their own indexing solution off the ground. If an alternative search engine reached Bing's level of popularity, this would undoubtedly happen.
The same goes for DuckDuckGo and others. All of the above use the Bing search API for the majority of their web results which for most use cases is not economically sustainable.
I do think there is a large swath of users who will pay a subscription for a truly great search engine offering, but indexing has to be at the core of this offering, at least for me. If users realized this is just Bing results with a few enhancements and additional result sources mixed in, they might not be as willing to pay for what they could technically get for free elsewhere, albeit with significantly less privacy.
That said I wish Kagi all the luck in the world. As the original dev who planned out and built the initial backend implementation in Crystal and put together their early engineering team, I can at least say they are building on rock-solid, very fast and privacy-oriented foundations, and this is a truly web-scale product in terms of the infrastructure design.