These are low priority objections.
This is a thread about search quality, and neither of your objections lower search quality.
Further, neither of the objections makes any difference in the practical world where Google ties the search terms to your account, and you don't have to log in to search, in the same sense that you don't log in to Google to have your search terms tied to you. After using kagi, then you just use kagi, and they don't save your terms.
Finally, Google has assertions in the TOS you agreed to about what they can do with your searches. So does Kagi. If you do care about search terms tied to you, you're welcome to read those and understand who has concern or liability for what aspects of your privacy.