“But if people had not ‘seen’ that integrity, they would not have hung around long enough to hear.”

I am not sure where this is biblical? Can God not save anyone he chooses in any way he chooses? John 6:44 says God draws us to him, we do not choose to be saved. We can never come to saving faith without Gods choosing us to be saved. We are dead in sin, not wounded by sin.

“No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day.” (John 6:44 ESV)

“even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption to himself as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace, with which he has blessed us in the Beloved.” (Ephesians 1:4-6 ESV)

I still see a works based theology in your description. That we do something to compel people to Christ instead of Christ. John 6:44 says the opposite.

With regard to modelling the ‘role’, that is how we learn, we listen and we forget, we see and we learn and then when we finally ‘do’ what Jesus asks, finally we understand. Jn. 8:31 ff. Simply good discipling, or teaching practice. And as for the Acts of the apostles, the clue is in the name isn’t it? They ‘acted’ on that same integrity and did all the things Jesus did.

Can you make an engineer, artist, mailman etc. by just modeling it?

Teaching all that Jesus commands requires preaching and having conversations. Godly preaching is not talking down to others but telling gods truths.

Did Stephen, Peter, Paul model or preach. Look at the book of acts, they preached and taught instead of modeling. Just because some preachers are jerks doesn’t mean it is wrong to preach and teach.

True faith and understanding has to be ‘caught’ rather than taught. You cannot build God’s kingdom on your own, so discipleship is necessary, but more effective when you follow Jesus’ example, without ‘judging’ or preaching down to others.