I think we need to regain a healthy, biblical view of interruption.
Interruption can be good or bad. When I'm hurt and a doctor tells me I need to go to the emergency room, that's a good interruption. When I'm leading family worship and I get a recorded phone call from a politician, it's a bad interruption. Much open-air preaching is bad interruption. Sometimes very judgmental. Even cruel. Good open-air preaching, humble and loving preaching, would be the best interruption we could ever have.
God has called us to the mission of good interruption. We don't need permission. We don't need to find an invitation to speak. We speak. We declare. We preach. We have been given the command to interrupt the world before they face the judgment of God. We are physicians crying out to a sick world to get life-saving medicine. We are ambassadors of another Kingdom warning that the current Kingdom will be destroyed and the only rescue is to join the Kingdom of the Good King. That's what the Gospel does. It forces the issue. It interrupts.
Praise God, the Gospel interrupts with power. The Bible tells us we have the power of the Gospel for salvation, the power of the Holy Spirit to be witnesses. We have the Word that is fire and a hammer that shatters the rock and won't return empty but accomplishes what God's purpose for it. We have a sword that separates joints from marrow, the sword of the Spirit. God doesn't give us an ineffective Word, but an effective one. It saves.
If we have this power at our fingertips as preachers, and given God's permission to interrupt the lives of everyone around us, how can we not preach to everyone? How can we be content to confine our preaching to those who show up?
(Check out all my posts & resources on open-air preaching)