So we did exactly this when we dropped our Prime membership a few years ago as part of working against Amazon building a massive warehouse in our fully residential borough (we won if anyone was wondering, they chose not to continue fighting it in court). We shop mostly in store at Target and other brick and mortar stores. We will also shop online still, but almost always directly from the manufacturer. This usually means paying shipping, but I figure our UPS driver and mail person need a paycheck too so we are fine with that. We will occasionally use Amazon for things that are just hard to find elsewhere but only order once our cart is in the free shipping price range. It turns out, Amazon is not only a shit company the uses dark patterns to push a mostly superfluous subscription, most things we buy are cheaper elsewhere. Combined with not buying nearly as much random crap, we have saved a butt load since quitting Amazon.
Kagi doesn’t hide that they use API calls to multiple sources for each search, they are fairly upfront about honestly. The benefits of use Jagi IME are the results are great, the site is fast and gets out of the way, it’s fairly affordable for what it provides, and the goals of the company is in line with mine (namely to find a thing I’m searching for). They are well funded enough to give me confidence that I’m not going to have to configure yet another search engine, and the integrate into pretty much all my access points easily as a default search engine.
I have seen no reason to think they abuse their position to impact my privacy, and bring closed source does not automatically make them evil. You included no alternatives that are open source, and the ones I explored were either difficult to get setup, required me to run something on my own infrastructure, or didn’t provide the integrations or results I expect. Kagi does.
Kagi isn’t perfect, and there are a ton of suggestions on their feature tracker that users rightly want implemented (including open sourcing more of their code-base). But as a paid search engine that makes me not the product, it does that job well.