If you compare the Professional plan (unlimited searches), to the API, you could justify that the extra AI cost is negligable if you are heavy user. The API costs $12 per 1000 searches, so 1.2¢ per individual search. 10/0.0012≈833.33. At 834 searches or more you would not be paying for the AI features. Obviously, this is only a comparison to the API, which might not have all special Kagi features.

But if you're using the starter plan, which is 300 searches for $5, then you definitely do pay for the assistant. The API cost would be $3.60.