1) He uses the present tense throughout the passage.
"I am of flesh..."
"For what I am doing, I do not understand; for I am not practicing what I would like to do, but I am doing the very thing I hate."
If the competing views are true, we'd expect to see verbiage more like this:
14For we know that the Law is spiritual, but I was of flesh, sold into bondage to sin. 15For what I was doing, I did not understand; for I was not practicing what I would have liked to do, but I was doing the very thing I hated. 16But if I did the very thing I did not want to do, I agreed with the Law, confessing that the Law is good. 17So now, no longer was I the one doing it, but sin which dwelt in me. 18For I knew that nothing good dwelt in me, that is, in my flesh; for the willing was present in me, but the doing of the good was not. 19For the good that I wanted, I did not do, but I practiced the very evil that I did not want. 20But if I was doing the very thing I did not want, I was no longer the one doing it, but sin which dwelt in me.But we don't. The present tense maintains throughout.
2) Paul already discussed what it was like when he didn't know Jesus, when he was under the condemnation of the Law, in verses 7-13.
3) Verse 15b says: "I am not practicing what I would like to do, but I am doing the very thing I hate..."
18b: "...the willing is present in me..."
19: "For the good that I want..."
19b: "...practice the very evil that I do not want..."
20: "But if I am doing the very thing I do not want..."
21: "...the one who wants to do good..."
The only person about whom it is true to say that he wants to do good, hates evil, is willing to do good, etc, is the regenerate person. How do we know this?
Romans 8:6-8 - For the mind set on the flesh is death, but the mind set on the Spirit is life and peace, because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able to do so, and those who are in the flesh cannot please God.
Does doing good, being willing to do good, desiring not to do evil, and such things please God? Yes, of course.
And the only way that one can escape from being in the flesh are those who are born again by the Spirit of God, those who are alive in Christ. One is either alive in Christ or dead in sin, and those who are dead in sin and in the flesh cannot please God, and these statements Paul makes in Romans 7 are inapplicable to them.
4) Even if Paul is speaking about himself as under the Mosaic Law or as before he knew Jesus, he still affirms total depravity here. "Nothing good dwells in me..."
5) Verse 23 ("I see a different law in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin which is in my members") does not make sense unless there exists a battle, a duel between good and evil, in the regenerate person. Lost, unregenerate sinners don't battle against sin, and they follow the lusts of their glands/bodies/hearts/evil thoughts without much compunction.
6) Paul does not cry out for mercy from the Law or to be born again at the end of his discussion. Rather, he cries out for deliverance from the body of this death. The sinful nature remains in his flesh, he feels the weight of the struggle, and he longs to be free from his body (ie, to die and be with the Lord and thus free from the presence and temptation of sin) so as to be released from this struggle.
DISCLAIMER: In no way is any of the above intended to excuse sin, diminish sin's severity, or deny that regenerate people are able to do the right thing and can deny temptation every single time that temptation arises.