Paul isn't himself in Rom 7:7-25. He's Adam in the first half and a Medea-character in the second. He assumes these personas because they serve his argumentative purposes perfectly. His chief aim in Rom 7:7-25 is to assure the Jews in Rome that God always acted for the good in giving the law; and to correct the perverse claim of Gal 3:19-24, where the law is an active agent consigning Israel to sin, and where God intends such a result "so that" he may save on another basis.
By taking on the role of Adam (vv 7-13), Paul is able to shift the blame for disobedience onto the power sin itself (~the serpent), exonerate God, and make the law passive in its relationship to sin. Sin (~the serpent) uses the commandment as a host, as it were, and foils God's intent.
By taking on the role of "Medea" (vv 14-25), Paul is able to go a step further and remove the law from sin's influence entirely. Sin now invades human flesh directly, using people as hosts, and turning them into pagans -- unable to do what they know to be right.
These are the shifts in thought spotted by E.P. Sanders long ago in Paul, the Law, and the Jewish People (p 75), though Sanders didn't make the Adam/Medea associations. Making these associations lends considerable force to his argument.
The Lutherans are right about one thing: Paul speaks about the law phenomenologically and targets Jews in Rom 7. Gentiles were dealt with in the previous chapter. Pagans die to ungodliness (Rom 6:16-23) -- to "impurity and lawlessness" (Rom 6:19) -- while Jews die to the law (Rom 7:1-6). But that implies that the law is equivalent to ungodliness. Rom 7:7-25 clarifies accordingly. But as Paul saves the law, he damns Israel instead, turning the Jewish people into wretched pagans (vv 14-25) who are unable to control their passions and do what the law requires.
Rom 7:7-25 might be called an exercise in theological give-and-take. Do we prefer a God who is sovereign but perverse (Gal 3:19-24) or benign but incompetent (Rom 7:7-25)? Were the Jewish people robust and capable (Philip 3:4b-6) or as hopeless as pagans (Rom 7:14-25)? It depends on the ox being gored.