"Given, the hard heart of King Saul, why did God chose him to be the first Earthly King of Israel?", I asked a mentor of mine who is a Pastor. He said that King Saul changed when he became a king. Maybe Saul was a very nice person before he became king but I think he had a wicked heart before then it was just not evident because he did not have the power that comes with kingship.
The second king, David was also chosen by God and all his life, he whole heartedly followed God.
In our secular world, we see leaders who are voted in, some took power by force through armed conflict and the like. We can ask if everyone of our leaders are chosen by God. Why would God put leaders who are wicked; those who do not care for the rights of people, do not care for justice and righteousness, do not care for the poor but are greedy, selfish and arrogant.
But, then one remembers that there is nothing that God is not aware of. Our responsibility is to respect all those in authority. If King David would refuse to kill or disrespect a king as wicked as king Saul, because of the fear of the Lord, his attitude is worth learning from; he became a great a leader.
A leader must first be a follower who respects authority because of the fear of God. Our attitude towards people who have been placed in the position of authority over us must be one of respect. God has the heart of kings in His hands. It is better to take your concerns to Him. Put your hope in God.