Psalm 143: David's acknowledgment of God's truth and righteousness

Verses 1-2: 

Lord, hear my prayer, listen to my cry for mercy; in your faithfulness and righteousness come to my relief. Do not bring your servant into judgment, for no one living is righteous before you.

When David prayed for deliverance from his troubles, he did not appeal based on his own goodness and righteousness. If God were to save David, who is suffering despite being a good person, it would not be because of God's truth and righteousness. David does not claim to be righteous. Instead, he praises God as being truthful and righteous, who hears the prayer of the sinner and seeks to save. In verse 11, David knows the goodness that swallows up evil as the name of God: "For your name’s sake, Lord, preserve my life”. Let's believe in a God who grants salvation not because a person is righteous, or asks for forgiveness of sin, but even when they do not repent or live righteously. Who would not ask for forgiveness of their sins when such a God suddenly approaches? Who would not praise the God who has saved them?