Proof by reality. Given that at the time it was written they were trying to get rid of king the idea that the verse says “don’t get rid of a king” is laughable. It is saying that if they won that was God’s will, and if they replace him, also God’s will. And if they don’t ALSO God’s will.
Those are the facts. You are wrong. Your own carefully selected verse says we can get rid monarchs. Period. Bye
Repeat of proof by assertion. Something does not become a fact by your say-so; we aren’t in Airstrip One.
Absalom for a time won the crown of Israel by force, but it was not God’s will for him to be the king; same with Adonijah versus Solomon.