... a problem of someone with an unlimited searches account sharing such link on reddit.
True. A system that allows that would not satisfy the "someone is paying for it" condition.
There, someone is buying a plan for themselves, but unlimited plans are clearly not for sharing. In a system where sharing exists, unlimited plans might be called personal plans instead.
As long as a search is associated with a limited plan, I think that would count as "someone is paying for it". What if unlimited/personal plans simply don't get to use the share feature?
... in any case there would need to be a special link
Not necessarily. For example, identifying devices or the networks they connect from may be sufficient to associate them with an account. In that case, the account holder would configure sharing by adding those identifers instead of generating links.
So the goal needs to be further defined - is it to get new users to try Kagi? If so, extending trial (via referral program) may be a path forward.
It is, but I was making a distinction between users and accounts. Obviously there must be an account in order to do billing, but if multiple users can benefit from it, they could have a more frictionless experience.
Let's consider the case of a company or other organization that wants to provide Kagi to all of its members. It would be good if a single account could cover all searches done from the org's network. That way, the individual users wouldn't need to do any setup at all.