

Banks don’t really create it out of thin air. Banks are letting you borrow money they otherwise hold, meaning they can’t lend indefinitely. This is the exact same way say a library works, they can only lend you books they have, and while you are using that book they cannot lend it to others. Paying back the principal on your loan doesn’t make the money disappear, it’s you giving back the amount you borrowed, plus extra to compensate the bank for lending you the money. This all matters a bit more in non-fiat currencies since those are backed by something intrinsically valued (such as gold), but even in fiat currencies banks that lend more money than they have access too are over extended and generally need to borrow themselves from either other institutions or the Fed in the US. This is why the Fed interest rate impacts loan rates.
While I understand the note on Kagi requiring an account making it less private in theory, in practice you can pay using OpenNode and use an anonymous email to sign up which makes it impossible to really tie anything to the real person you are at that point (and functionally like other engines that may use backend fingerprinting to help personalize your results, just in the open).
Kagi provides a bit more detail in their FAQs: https://help.kagi.com/kagi/faq/faq.html#why-trust
That said it’s still an American company, so that may be the deal breaker for some which is fair.