The sacrifice pleasing to God is a broken spirit. God, You will not despise a broken and humbled heart.
Psalm 51:17

Brokenness – stricken, wounded, dismayed, to be grieved, to make sad

In Psalms 51:15-17, David is consumed with guilt.  He is in anguish and would do almost anything to escape from it.  What God really desires from David (and from us!) is only that we are truly broken over our sin.  David would have offered sacrifices. Sometimes we try to take the easy way.  We try to negotiate with God—offer a sacrifice of sorts.  But God looks at the heart.  He looks for true repentance, a deep sorrow.  God wants a heart pliable to His Word, one that trembles at His Word, tender and obedient.  In other words, God seeks a broken and contrite heart.  Man may despise what is broken but God does not.  Instead, He looks with favor upon a broken and humble attitude.

But this is the man to whom I will look and have regard: he who is humble
and of a broken or wounded spirit, and who trembles at My word and reveres My commands.
Isaiah 66:2b AMP

God chooses to dwell among the humble because they have a reverent attitude. All of our wrong doing comes to a climax at the foot of the Throne.  Our faith and repentance glorify God.

The Lord is close to those who are of a broken heart
and saves such as are crushed with sorrow for sin
and are humbly and thoroughly penitent.
Psalm 34:18 AMP

Brokenness—to be stricken, wounded, grieved by our sin—that is what God desires.