I agree the law's purpose was in itself not to make us blessed but as you equate after this it is essentially a foundation of the old covenant that upon keeping it included blessing so separating it from being the source of being blessed doesn't really totally work. Personally I think the blessing was from following God (in faith) and God used the law in a fashion to test the people sort of like putting them in a fence and seeing which side they would jump off of it on, with the Law as the fence itself.
I do see blessing equated in the OT via the law but not directly but through keeping it under the old covenant God blessed Israel as a nation, or punished (cursed) them for breaking it including sending them into slavery at the hands of enemies. I think on a personal level one is cursed with punishment for breaking the law in Paul's time sometimes it meant death by stoning in some instances. I think Paul saw overall that there was nothing to be gained by the law once the gospel of grace revealed to him said it was not an integral part of the new covenant and that the blessings did not outweigh the curses as breaking the law was not a 50/50 blessing/curse deal with God. Contracts tend to need to be mostly fulfilled for the party to pay off the other in the end (blessing) and the covenant with the law required the nation to participate properly not just certain individuals.
St. Paul himself recognized that there was a serious problem with attempting to keep the law. He spoke of that problem quite candidly:
We know that the law is spiritual; but I am unspiritual, sold as a slave to sin. I do not understand what I do. For what I want to do, I do not do, but what I hate I do. And if I do what I do not want to do, I agree that the law is good. As it is, it is no longer I myself who do it, but it is sin living in me. I know that nothing good lives in me, that is, in my sinful nature. For I have the desire to do what is good, but I cannot carry it out. For what I do is not the good I want to do; no, the evil I do not want to do - this I keep on doing. Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it.
So I find this law at work: When I want to do good, evil is right there with me. For in my inner being I delight in God's law; but I see another law at work in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin at work within my members. What a wretched man I am! Who will rescue me from this body of death? Thanks be to God - through Jesus Christ our Lord! (Romans 7:14-24a,NIV)
2,000 years later psychologists have given what St. Paul described a name; it's called 'paradoxical intention', and it is universal among all people. Basically, it is a quirk in our nature that condemns to failure anything that we consciously try to do. Psychologists have even used it in the treatment of their patients ("Try to stay awake," told to those with mild insomnia and "Try to get writer's cramp," told to those whose profession requires them to write, but they find themselves afflicted with this problem, are just two examples). It is also the basis for the saying I first heard decades ago; "The harder you try, the faster you fail."
So like our salvation, our words and actions must depend not on what we ourselves can accomplish, but what God himself can accomplish. Since our following a set of laws is doomed to failure because of this inherent flaw in our psyche, God has seen fit to 'rein in' our sinful nature himself, and then replace that nature with a new, spiritual nature:
So I say, live by the Spirit, and you will not gratify the desires of the sinful nature. For the sinful nature desires what is contrary to the Spirit, and the Spirit what is contrary to the sinful nature. They are in conflict with each other, so that you do not do what you want. But if you are led by the Spirit, you are not under law.
The acts of the sinful nature are obvious: sexual immorality, impurity and debauchery; idolatry and witchcraft; hatred, discord, jealousy, fits of rage, selfish ambition, dissensions, factions and envy; drunkenness, orgies, and the like. I warn you, as I did before, that those who live like this will not inherit the kingdom of God.
But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control. Against such things there is no law. Those who belong to Christ Jesus have crucified the sinful nature with its passions and desires. Since we live by the Spirit, let us keep in step with the Spirit. Let us not become conceited, provoking and envying each other. (Galatians 5:16-26,NIV)
At first this looks like a list of Do's and Do Not's. But looking at it more closely, we realize that many of 'the acts of the sinful nature' are the emotions which are the very foundation of our old natures. For us to replace our own emotional base can be compared to a leopard trying to exchange its spots for the stripes of a tiger. It can't be done by us; we need outside help in order to bring these base emotions under subjection. And this outside help is the direct intervention of the Spirit in order to 'rewire' us so that we can live our lives in accordance with God's will.
It is the Spirit, rather than we ourselves, who 'reins in' our sinful nature. As the first paragraph of this passage states, he is the one doing battle with it, and our part is to follow dutifully behind him as he continues to advance on it.
But he doesn't stop with merely conquering our sinful nature. Instead, he implants in us a new nature (the fruit of the Spirit). It is these 'fruit' that enable us to say and do what conforms to God's will. It is against these 'fruit' that there is no law, because those who have their lives governed by them have fulfilled the spirit of that law. And they have fulfilled it not through trying to keep laws and commandments, but rather through their new nature's automatically being 'in synch' with the spirit of that law.
We all know that if our intellect wants us to either perform a certain act, or refrain from performing that act, but our emotional core desires that we do the opposite, we will in all probability do what our emotions dictate rather than what our intellect dictates. Our emotional core is simply too strong for us to resist its advances. That's why we need to have that emotional core itself brought 'in line' with what God wants of us, or else we cannot say and do what God wants of us. It is when that emotional core itself 'pushes' us to say and do what God wants of us that the job gets done.
God knows this. That's why he sends his Spirit to engage our sinful nature in battle, defeat it, and replace its influence over our lives with his own influence (the fruit of the Spirit). So like our salvation, the words and actions which we say and do following our accepting that salvation are dependent on him. And this is as it should be, because it 'slams the door' on the most dangerous attitude that anyone can possess, namely, the attitude of being proud.
It is accepted that the most dangerous sin is the sin of Pride. But by making our salvation dependent on our accepting what he has done, and by making our words and action also dependent on our trusting his power to himself alter our nature so that it now conforms to what he wants of us, he has eliminated any reason for us to boast. Our salvation was earned by him and then presented to us as a free gift. Our new nature was also earned by him and implanted within us as another free gift. The credit for both is entirely God's, with us as merely the recipients of those gifts.
