unfaithful kings

In the Old Testament, people never seem to be able to avoid upsetting God. In the First Book of Samuel, Saul becomes king. He is from an unimportant family in a small tribe, and God chooses him to rule Israel. He seems to be innocent, but when he gains power he becomes sinful. Instead of killing all the Amalekites like God tells him to, he spares the best livestock to sacrifice to God. God becomes upset that Saul did not obey him, and regrets choosing him as king. David seems like a good replacement for Saul, but he also becomes corrupt. He becomes greedy and seduces his neighbor's wife Bethsheba, "though she was still purifying herself after her period" (11:4). After that wrong, he makes it worse by trying to hide it and sending Bethsheba's husband off to battle to die. The Lord again becomes upset and punishes David by killing his first son. These events make me wonder why God chose these people to be kings in the first place, since they are going to end up sinning and causing God to regret his decision. Also, why does God keep testing people for their faith when they seem to fail every time?