***I generally agree but I think there's room for some evangelism in our worship.***
Let me build on what I was trying to say.
In any given church, there are saved and unsaved. The saved are there to worship, the unsaved have all sorts of bad reasons for attending. Some think the very act of going to church will save them.. Others go just because they want to be a good example for their kids. The list goes on and on. The tricky thing is that you really don't know if the guy sitting next to you, or teaching you Sunday School is saved or not.
In my walk I have come to appreciate something called "Law and Gospel" worship.
The way it is preached works out something like this: The first part of the sermon focuses on God's law and our rebellion. It closes with God's answer to our rebellion, the life, suffering and resurrection of our Lord and Savior.
The saved benefit in that they hear a law that no longer condemns but provides for our sanctification. And when we fail it is reinforced that the Gospel is for Christians and the unsaved.
The unsaved elect hear the law, realize that they are unsaved, and then are able to see that their own efforts are nothing but filthy rags. They will see that Christ is their only hope in this life and the next.
The problem is in many churches the meditation/message (in seeker sensitive terms) focuses on morality, which is the Law, but watered down so it sounds like something we can achieve. Just so the seeker isn't offended, the full measure of God and the full measure of Christ's sacrifice are not preached. People walk out and in a Pelagian response think "I'm a good guy, I can do that!" And then they flip off the guy who cuts him off on the way to the Golden Corral. They might have some idea they shouldn't have done that. But they promise to try harder.
A Christian who gets cut off might feel some anger, or might even flip the offender off. But after hearing the Law and Gospel realizes they have sinned and pray that God will move them past that sin in their life (sanctification). They die more and more to their old selves and live to Christ.
In a rambling way, I am trying to say that the preaching of the word has an Evangelistic effect on the unsaved, and a sanctifying effect on the elect.