I think, in your study of law, you need to read the 119th psalm. That psalm explains the law, and it certainly does not say that the true intent of the law is to tell us we can't obey it. The law is God's word, it leads us to Christ, it guides us as we walk with the Lord. When we seek the Lord with all our hearts, then we look to the law to guide us in our walk.
I agree with your post, except that it limits the law, and God's word should never be limited.
The law justifies no one. The law has one purpose and that is to lead us to Christ. The law is not made for the righteous. Now if you are not righteous, then you have no business calling yourself a Christian.
1 Timothy 1:9-11
"We realize that law is not enacted for the righteous, but for the lawless and rebellious, for the ungodly and sinful, for the unholy and profane, for killers of father or mother, for murderers, for the sexually immoral, for homosexuals, for slave traders and liars and perjurers, and for anyone else who is averse to sound teaching that agrees with the glorious gospel of the blessed God, with which I have been entrusted.…"
There are 613 commandments. Which ones apply to you? Some are women only or for the priests. You must obey every single one, without exception, or you are lost. Except you cannot. There is no one who can sacrifice animals to atone for your sin. Hebrews tells us that the Law is the shadow. Live there if you prefer. Me, I like to live in the light.