It's still in the confessions because Luther and the early Reformers were all ex-Catholic monks and such, and didn't let go of their upbringing easily. But scripture plainly shows that we confess our sins to God, and he is just, and will forgive us. In fact, they use one of the Psalms (see what you quoted) to support the stance that one cannot enumerate each and every sin. It's this part of Catholicism that causes such terrible guilt in most Catholics. We live by grace, we are justified by Christ. We don't live under sin any longer.
What drove Luther from the church was that he could not understand how one could be forgiven and yet still feel such constant, oppressive guilt. He was going to Confession so many times a day that the priest acting as his confessor once said to him, "Brother Martin, it is not necessary for you to confess every fart." It was this that made him turn to the scriptures and find there the simple message - we are saved by grace, through faith, not by how good or bad we behave - we cannot save ourselves through trying to be "good enough" - we can never be good enough. And before you lob out the antinomian argument, I suggest you read the Lutheran Confessions and the history of Luther's argument, because you can find all the details there that I don't have time or energy to even begin to start reiterating here. But Luther knew that "even while we were yet sinners, Christ died for us."
That is a sin of presumption: refusal to believe in sacramental absolution. Related to that is apparent Luther's scrupulosity. Should every compulsive sinner start his own church, or was Luther somehow special?