WHAT EVANGELISM IS NOT.
I believe you. Invitation to programs and church services is not evangelism. Evangelism is about leading the unbeliever to repentance. It is sharing the love of Christ and letting the unbeliever know God and believe in the Lord Jesus Christ. When you have a flux of people invited to church, for example, believing that the undiluted Word is taught in that congregation, hoping the people get born again is not a bad idea. However, that is not true evangelism, as you rightly pointed out.
Evangelism is for the lost souls, and not the qualified. God does not call the qualified. According to 2 Corinthians 3:5, We are not qualified in any way for us to decide who should be evangelized to. We have no right to judge anyone—for example, a dead criminal who had killed lots of people. If the love of God is pointed at him, we have no right to deprive him of getting the gospel. As you said, No one has the right to run down an unbeliever.
Salvation is a miraculous work of God, not of any man. Hence, no man should take credit for it. No man is born an “evangelist,” nothing like I have the gift of evangelism. You evangelize based on your encounter with Jesus Christ. It’s the experience of the Love of Christ that makes the gospel. If someone gets born again in the process, it has nothing to do with your, ability or capability.