God doesn't just want you to feel better.
God actually wants you to get better.
Saul never took a step to actually get better.
Be gracious to me, God, according to your faithful love; according to your abundant compassion, blot out my rebellion. - Psalm 51:1
Completely wash away my guilt and cleanse me from my sin. 3For I am conscious of my rebellion, and my sin is always before me. Against you — you alone — I have sinned and done this evil in your sight. So you are right when you pass sentence; you are blameless when you judge. - Psalm 51:2-4
Let me hear joy and gladness; let the bones you have crushed rejoice. - Psalm 51:8
Restore the joy of your salvation to me, and sustain me by giving me a willing spirit. 13Then I will teach the rebellious your ways, and sinners will return to you. - Psalm 51:12-13
You do not want a sacrifice, or I would give it; you are not pleased with a burnt offering. 17The sacrifice pleasing to God is a broken spirit. You will not despise a broken and humbled heart, God. - Psalm 51:16-17
David wanted to embrace the process of getting better.