Not long ago someone asked me if I thought the purpose of God's law was to curtail unrighteous and criminal acts (which was this person's interpretation/understanding of 1 Tim 1:8-10) and to teach the people of Israel not to do wrong. My response is that the role of the law was to condemn sinful acts, but it could do nothing to curtail sinful acts. Even under the law, "there is no one righteous, not even one... There is no one who seeks after God... There is no one who does good, not even one." The law has no power to make a bad person good, nor to change a person's bad behavior to good. In fact, not only could the law not curtail sin, but "the law is the strength of sin." (1 Cor 15:56).
The word "curtail" means to cut back, diminish, reduce. Paul said that the law actually has the opposite effect. "The law entered that sin might increase." (Rom 5:20). "But sin, taking opportunity by the commandment, produced in me coveting of every kind." (Rom 7:8) "When the commandment came, sin revived and I died." (Rom 7:9) "And the commandment, which was to bring life, I found to bring death." (Rom 7:10)
1 Tim 1:8-10 (the lawful use of the law) doesn't say that the law leads to a curtailing of sin. If we put Paul's words here alongside everything else he says about the law, we see that the law is a tutor to lead people to Christ. (Gal 3:24). (Not to lead people to better behavior, but to Christ.) Paul goes on: "Therefore the law was our tutor to lead us to Christ, that we might be justified by faith." That was the purpose of the law. To lead the lawless and subordinate, the ungodly and sinners, the unholy and profane... etc, etc... to Christ, that they might be justified by faith.
"But to him who does not work but believes on Him who justifies the ungodly, his faith is accounted for righteousness." (Rom 4:5)
The requirement of the law was perfection, and yet it had absolutely no power to provide it! Perfection could not be obtained through the keeping of the law. The law only showed people their imperfection, and led them away from trying to be perfect through their works. It pointed them to being made perfect, righteous and holy by the gift of God, by His grace alone, through faith. What teaches us to do right and to say "no" to sin? It's not law. It's grace! (Titus 2:11-14)
Even with all of this being said, I must point out something very important. As Gentiles (which is a word that refers to all people who are not Jewish; that is, most people who have ever lived), we never had any relationship to God's law in the first place. We were strangers and aliens from everything that had to do with Israel and the law (Eph 2:12). We were without hope and without God in the world. We were "far off" from God (Eph 2:13). But in Christ we have been brought near to Him. As Gentiles, we came to God, not through the tutor of the law like Israel did, but simply by God inviting us into the New Covenant by grace, through faith. There actually is no "lawful use" of God's law when it comes to Gentiles. The lawful use of God's law is for Jewish people who are trusting in their own works for righteousness. For Gentile unbelievers, it's not a matter of law but a matter of conscience. (Rom 2:12-16)