I'd like to be warned before hitting a hard limit, in whichever way. E.g. warning emails ("You've reached 80% of your quota"), or a meter on the search page.
From a higher POV, I like GPT-4's smaller time windows way better (x queries within 4 hour window). I hate to be "locked out" of search for a whole week. A few hours wouldn't feel that bad.
Kagi are very open about their policy to submit feedback, bugs, and feature requests at https://kagifeedback.org/. I've not submitted anything Kagi Search, but I've submitted a few features and performance issues/bugs to their Orion feedback. I got replies from Vlad and Kagi employees within 12 hours. Feel free to suggest this as feedback I'd say...
You can set your own notices in Kagi and you are never locked out of searching (as you can adjust limits yourself). We do not plan to invest more in these features as we'd like to walk towards the world where we can remove limits again.