It costs money, which is how they can be an actual search engine rather than an ad portal that pretends to be a search engine.
I have seen the future. Crap is free. Endless amounts of crap. Soon all this crap will be AI generated and designed to addict you. If you want anything that is not crap you will have to pay for it.
I'm a huge fan of self-hosted and decentralized stuff but a search engine is an area where I can't think of a way to do such a thing. The bandwidth requirements for continuous spidering and the data storage requirements are too high, and if you tried to distribute it you'd end up with an absurdly chatty protocol that couldn't be used by anyone with anything short of an unmetered full duplex fiber link.
The next best thing is a company that I pay to be a search engine for me and does that without trying to shove ads at me.
The complaint is still valid. I have subscriptions to a few sites, mostly news. I get why I need to login, otherwise how would they know that I've paid. It's still a pretty poor experience, I pay for a service, and now I need to fiddle with the settings in my browser so the site I pay for can remember my credentials.
I get that part of the issue is that I keep a weird privacy focused configuration in my browsers and delete cookies when I close the browser, still it results in poor user experience, for a service that I pay for. I don't have any good suggestion on how to fix it, but it's is valid to complain about having to sign in.
It's a poor user experience because you break it on purpose. Whatever other way they can come up with to permanently identify you, you will block that in the name of privacy and keep complaining.
I don't really care about privacy from a company that already have my credit card information, and real name and address in most cases. I care about privacy from "the others", and the paid services is collateral damage. It does appear from another comment that Kagi actually thought about it and allows a token in the search URI, that's pretty neat.
You can get an access token from settings which can be provided in the URL. Set your search engine URL to include the token, and your searches just work, even in Private / Incognito.
yeah they are one of those weird businesses that provides services in exchange for money. They say it costs them $12.50 to serve 1000 queries and the fee isnt that much more.
There used to be some sample searches on their blog but it looks like those are also paywalled. wonder if that was intentional.
I am not affiliated with them.