The invitation given at the end of modern American services, is not a practice found in the New Testament. Research shows the invitation is inherited from the denominational altar call created during the Second Great Awakening. The altar call was a technique utilized to bypass the mind into the heart to create an instant decision. It is not a fit practice to make diciples, but it can get someone to come down an isle.
The one usually given the most credit for the practice is Charles Finney. The modern church views him as the father of evangelism. I do not consider this a title of distinction but rather ignominy as it has lead to the emotion based seeker sensitive practices of the modern church.
The modern invitation is rooted in revivalism. The creation of worship bands, asking Jesus into the heart, tongue speaking and dispensationalism all came into the church about 150 years ago. If you except the invitation you should be consistent and accept these other non-biblical practices as well. They all work hand in hand to bypass conviction to manipulate emotions instead of reaching the mind.
Known as an expert in all he surveys, he freely shares his opinions on politics, science & theology using diatribes based upon careless research from tertiary sources that presupposed what he thought in the first place.