There are some here that would agree with you. Personally, taking the verse to deal with the nature of man would take the verse out of context (Paul transitioning from the contract between the righteousness of the Law and the Righteousness of faith into the opportunity to believe) – but Paul does present the importance of the cognitive message.
Paul asserted (in the previous verses) that one must call on the Lord to be saved. He then begins to outline the steps that fulfill calling on the Lord. Of course, Paul does continue by stating that Israel has certainly heard the gospel – He has stretched out his hands all day long to a disobedient and recalcitrant people (hearing the gospel apparently was not their inability).
Men can choose to listen or not. That is not inability, it is choice.
The only inability implied is that men cannot believe on him of whom they have not heard. Now here is the perfect place to mention any moral inability, but Paul does not say one word to that effect here, or anywhere in scripture.
So yes, of course teaching the gospel is important. While this has absolutely nothing to do with man being unable to believe on their own merit, I agree that we need to preach.
I think that the passages you need to combat are those Calvinists, Arminians, and others who believe in depravity. They include: Gen 6:5; Jer 17;9; Rom 3:10-18; Matt. 7:17-18; John 15:4-5; 1 Cor. 12:3; Matt. 13:14; John 1:11; John 8:43; Matt. 7:18;; John 6:44, etc. Those who believe in depravity do not deny the importance of preaching.
Gen 6:5 And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.
This verse simply states a fact, that men were wicked and their thoughts were continually wicked. It does not say one word about inability to repent. Noah was an exception to this wickedness, the scriptures say he was perfect in his generations and walked with God. This refutes inability.
Jer 17:9 The heart is deceitful above all things, and desperately wicked: who can know it?
This is a general statement and does not prove man is unable to repent from his wickedness. In fact, we see an example of this just 5 verses later.
Jer 17:14 Heal me, O LORD, and I shall be healed; save me, and I shall be saved: for thou art my praise.
So, within the same context we see men can repent and desire to be both healed and saved.
Romans 3 does not prove inability;
Rom 3:10 As it is written, There is none righteous, no, not one:
11 There is none that understandeth, there is none that seeketh after God.
12 They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.
If I were to say,
"None of my neighbors ever goes to church, no, not one" would you understand that to mean they were unable to go to church? NO, nobody would assume that, but that is exactly what folks do with Romans 3. It is simply stating facts about men, that they do not seek God, that they do not do good. It does not say one word about inability, people have been CONDITIONED by doctrine to read that into this scripture.
Mat 7:17-18 is easily refuted by Mat 12:33;
Mat 12:33 Either make the tree good, and his fruit good;
or else make the tree corrupt, and his fruit corrupt: for the tree is known by his fruit.
This verse shows men have both option and ability, they can make themselves good, or they can make themselves corrupt.
I could continue and go through every verse you have presented and show you they do not prove inability. The problem is that folks pull selected verses out of context to prove a doctrine, and ignore many other scriptures that refute it. This is a POOR way to study scripture.