Umm, subscription is actually the way Kagi monetises, instead of selling ads. This is exactly why you should consider it.
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.