William Burkitt on Romans 4:15

Here the apostle suggests another reason, why no justification can be executed by the law, because it condemns, rather than justifies. The law worketh wrath: that is, it discovers the wrath of God due to our transgression, and then pronounces condemnation upon the transgressor; for were there no law, either natural or revealed, there would be no transgression, and, consequently, no condemnation.

Here observe, 1. The use of the law; it discovers sin, it convinces of sin, it condemns for sin, it denounces the wrath of God due unto sin.

And note, 2. The apostle's arguments for the use of the law; he infers an utter impossibility of being justified by the law. That which condemns, cannot justify; but the law of God condemns the sinner for his transgression, therefore, it can never be the instrument and means of his justification.