There are several themes in Romans. The prominent is the fallen nature of mankind Gentiles addressed in chapter 1 and Jews in chapter. Then all have fallen and need redemption which chapter 3 covers. Then chapter 4 solidifies that we are all of the seed of Abraham by Faith in Jesus Christ. Then chapter 5 solidifies we are (all people) justified by Faith and then the comparison of the first Adam and the second Jesus Christ.
Chapters 6 & 7 speak of sanctification and chapter 8 ties it all together by emphasizing those who have the Spirit and live by the Spirit are co-heirs with Christ. Thus the called are justified, conformed to the image of Christ and eventually glorified.
Chapters 9-11 are certainly addressing how God in redemptive history has both chosen individuals and groups for His will and purpose.
I disagree with your summary of the letter to the Romans.
Romans 2:17
But if you bear the name “Jew” and rely upon the Law and boast in God...
Romans 3:1
Then what advantage has the Jew?
Romans 4:1
What then shall we say that Abraham, our forefather according to the flesh, has found?
Was Abraham your forefather?
Romans 5:20
The Law came in so that the transgression would increase...
Gentiles never had the law.
Romans 7:1
Or do you not know, brethren for I am speaking to those
who know the law...
Who knew the law?
Romans 7
4 Therefore,
my brethren, you also were made to die to the Law through the body of Christ, so that you might be joined to another.
The Gentiles were not under the law and were unable to die to the law.
Romans 9:1-5
I am telling the truth in Christ, I am not lying, my conscience testifies with me in the Holy Spirit, that I have great sorrow and unceasing grief in my heart. For I could wish that I myself were accursed,
separated from Christ for the sake of my brethren, my kinsmen according to the flesh, who are Israelites, to whom belongs the adoption as sons, and the glory and the covenants and the giving of the Law and the temple service and the promises, whose are the fathers, and from whom is the Christ according to the flesh, who is over all, God blessed forever. Amen.
What more needs to be said. Paul is pouring out his heart over his forsaken brethren, the Jews.
This is the reason and the purpose of the letter to the Romans, a long winded explanation of the failure of the nation of Israel to attain righteousness.
Romans 9:30-33
What shall we say then? That Gentiles, who did not pursue righteousness, attained righteousness, even the righteousness which is by faith;
but Israel, pursuing a law of righteousness, did not arrive at that law. Why? Because they did not pursue it by faith, but as though it were by works. They stumbled over the stumbling stone, just as it is written.
Romans 10:1
Brethren, my heart’s desire and my prayer to God for them is for their salvation...
Who is Paul talking about here?
Romans 10:21
But as for Israel He says, “All the day long I have stretched out My hands to a disobedient and obstinate people.”
Romans 11:1
I say then, God has not rejected His people, has He? May it never be! For I too am an Israelite, a descendant of Abraham, of the tribe of Benjamin.