Kagi currently uses Google and Bing in addition to their own index to serve you search results. They'll likely only use their own index once it's complete enough to be a replacement, as the API costs they pay to Google and Bing are not sustainable even with paying customers.

The advantage of Kagi being paid as opposed to being ad-supported is that you get unbiased results, or results with your own bias applied. You can set ratings for domains where you can set their priority in search results or even outright block them.

You can also setup redirects with regular expressions, so you could redirect youtube.com to piped.video for example.

And sure, you can emulate some of these features (like blocking sites from search results and redirects) using browser add-ons, but with Kagi this is integrated right into the search query, and as it's all server-side it works on all your devices. It's just very convenient.

Search always used to be free so I get that people find it discomforting having to pay $10/month for it (there's also a $5/month plan with 300 searches instead of unlimited), but $10/month for something I use dozens of times per day seems like a no-brainer to me.