To add, from what I understand at least, Kagi does build its own index for accessing smaller sites. To some extent, results are also served by a custom index, meaning some percentage of results do not come from [your disliked companies] and instead come directly from Kagi. It doesn't seem like a significant percentage of results come from that index, but it supposedly is still >0%.
Personally I mostly use Kagi for the ability to put Reddit on the bottom of the results, MDN to the top, and otherwise prioritize sites in ways that I want but which I know are purely based on my own opinions. It works well for my usecase, and I don't have to scroll through a bunch of sponsored links before finding my search results. Also, the recent integration with Wolfram|Alpha has been convenient with a couple of searches, like one where I needed the prime factors of some numbers.