I'd be willing to pay up to 3$ a month for my searches, but also per-use.
If I make 0 searches, why do I need to pay?
A replacement for Google that is to survive should really convince and be super cheap, it's so easy to ignore sponsored search results (for now).
Would you use your search engine more if every search query were an implicit microtransaction? Would you use it more or less if you had to consider that your first search of the month cost $3, or if it's the last day of the month and you need to search for something but you have to wait to not incur a full month's fee.
This is one of those arguments that sounds reasonable but isn't. Nothing but a flat fee structure makes sense for something you'll be doing hundreds if not thousands of times a month. And let's be real: if you're the kind of person who could go a full month with no web searches, you don't want or need what Kagi is offering.
And one way to "deal with" that is get used to it and forget about it unless you get some surprise hit (which can be avoided with a cap). But you'll have a warm glow feel that it's "fair"
It's not like this is some novel issue average people have never had exposure to (eg, utilities)