I haven't even heard of it so I don't have an opinion on it. If it works for you then great! Technically my private searxng is a paid service since I host it in the cloud but it does have the option to be free if you host it locally.

I'll also add, with a private instance of searxng you know for a fact nothing is getting saved.

I pay $5 a month to host my own instance of SearXNG on a 1GB Linode server. I am in full control of the server and the source code running it since it's completely open software. I don't have to trust that Kagi is being honest and hope that one day it comes out that they did something stupid like leak my data or sell my data through some convoluted legalese change to their terms of service.

Additionally I get access to search results from Bing, Google, DuckDuckGo, and any other provider I want, all without having anything about me or my activity tied to some kind of centralized identity/payment.