I do see your point.No, the law acted like a marriage license that enforced our submission to the desires of the flesh. Like how a wife, by reason of the law of marriage, must submit to her husband's desires. But, since the law of marriage that binds a wife to her husband is only in effect while the husband is alive, she is released from having to submit to the husband's desires when he dies.
And so it is with us. The flesh who once commanded our submission to it, by force of law, can not do that anymore because he's dead. The authority of the law that makes us serve the desires of the flesh ends with the death of the flesh. And so we are now free to be in marital submission to new husband and Master, Jesus Christ, and bear His fruit.
But even those not under the Mosaic Law were subject to their flesh too, before it was crucified with Christ. (with the affections and lusts, Gal 5:24)