My take: David recognizes that mere offerings to God can be shallow. What truly touches God is genuine emotion backed by truth. A broken spirit and contrite heart.
This causes me to think how they onboard and train a soldier in the military boot camp. They break him so they can properly build him. I see two paths to salvation in Scripture. One is planting the seed into a child when their hearts are softer and more pliable. They embrace and accept Him as a youth. The other way, the way I came into the fold, is the hard way. God requires each of His children to willingly accept Him and that starts with denying self. Our hearts, even as believers, are drawn away by the dark forces of this fallen world. God is drawn to the cry of His children who He will not despise.
He alone is able!
Abiding in Him, we are secure.
My prayer: Oh Lord, forgive me and keep me close to Thee.