The city transport system where I live has a subscription pass you can buy that is normally tied to a single person. However, if you pay a little bit extra you make the ticket transferable, and even let someone else travel with you for free on weekends and in the evenings. Like you say, they've presumably priced in the extra usage there that comes from it being transferable, or from the extra travellers, but also put limits on how much leeway you have to abuse the system.

I'm imagining rate limits that would prevent the user from making many more API calls than they would have made searches anyway. If you want unlimited 24/7 searches, you can pay for the credits directly, but if you just want to partially replace your existing search habits with e.g. interactive agent sessions, then that would be fine.

A more specific example would be how Anthropic allow certain Claude subscriptions to get free API credits, with some restrictions on the age of the account and with the number of credits being limited.

I think there is a workable solution here, although I can imagine that figuring out the details (how many credits to offer, what sort of limits, how to price the whole thing, etc) is complicated enough that Kagi have decided it's not worth the effort for the small number of users for whom this feature would be useful. And generally I'm very satisfied with Kagi, so I'm not complaining here or trying to suggest that this is something that they should be expected to offer. It would just be nice!