Rom 3:20 For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.
God's law tells us how we are designed to live, i.e. if we live according to the law, we will experience the life God created and designed us for. This is a good thing, not bad. Therefore, the law too is good. The law is simply God's operations manual for how mankind can best function according to his design and, therefore, to his optimal capacity, bringing the greatest honor to God and drawing others to him.
But in order for us to live according to the law, we must believe it is given by God for our good. So the problem isn't the law per se, it's our unbelief. We don't trust God, so we are unwilling to obey God and his directions for us. We believe our way is better than His.
Because we have no faith in God, we have no faith in his directions (the law) for us either.
As a result, the law actually reveals to us how we don't trust God; how we have rebelled and continue to rebel from believing God is our Creator, director, rightful owner, sustainer, provider, lover, caregiver, protector; the all-wise, all-powerful, always present, always loving, all benevolent, beautiful God.
If we knew and believed God was all of this for us and more -- i.e. exactly who he says he is -- doing as He says; following His direction; and obeying the law would be no problem.
Unbelief/distrust is our problem, not the law.
The heart of the law brings all of this out most clearly.
Jesus answered, "The most important (commandment) is, 'Hear, O Israel : The Lord our God, the Lord is one. And you shall love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.'
The second is this: 'You shall love your neighbor as yourself.' There is no other commandment greater than these." Mar 12:29-31
So are we good or worthless?
Rom 3:12 All have turned aside; together, they have become worthless; no one does good, not even one."
We are not worthless, but we become worthless when we don't do good.
"Salt is good, but if salt has lost its taste, how shall its saltiness be restored? It is of no use either for the soil or for the manure pile. It is thrown away. He who has ears to hear, let him hear." Jesus. Luk 14:34,35
We can do good because we are created in God's image. But because of our disconnection from God, i.e. our rebellious distrust/unbelief, we cannot do good for we were never designed to operate without God, separated from his love for us that empowers us to be loving.