Not promising it would work, but I would email support and ask to have the trial reset for your account. Companies are usually cool to restart trials if you ask.
But as I read the OP it is that he objects to the barrier of entry. He would prefer (possibly very harsh) rate limiting over the hassle of registrering an account. Maybe combined with a weak "nag" screen.
It might be hard implementing in a bulletproof way as IP restrictions are easy to circumvent. But it might be "good enough" to drive more adoption.
I'm a bit on the fence. It would be an interesting experiment.
If you want to hear from a happy Kagi user, I can say that I used Google thrice in the last two years, and it didn’t bring better results than Kagi.