Open air preaching is simply preaching in the outdoors, which all of those examples fulfill. There is also much of this in the book Acts, which was the primary way the gospel was spread.
Your illusion to needing to have a relationship with people or otherwise they will see preaching as a noisy gong is faulty, due to my previous point. There is no indication when Paul preached on Mars Hill that he had a relationship with those people. What about all of the times when the preacher was attacked, such as Stephen and Paul, since they are apparently ineffective, perhaps they should of done it in a different manner?
I reject all pragmatic premises on how we should evangelize, we should emulate the Scriptures and publicly preach, while at the same time do the naturally occurring good works and related speech to the gospel that would occur in our day to day life.
If being effective is sharing Biblical truth with the unbelieving then public preaching would definitely be quite effective at doing so. However if being effective is equal to how many "converts" one gets, than that is quite subjective.
It also opens a discussion on whether or not you believe that a dead in sins, child of wrath, who is at enmity with God is somehow more likely to truly be regenerated by God because there is a relationship with someone else.
The viewpoint could almost be guilty of glorifying the messenger above or equal to God, because apparently the conversion is dependent on having a relationship with the messenger, rather than the foolish means (preaching; 1 Corinthians 1) that God has chosen. Nowhere does Scripture teach that God using his foolish means is dependent on whether or not there is a relationship, it is not a prerequisite to God drawing a sinner to salvation.
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