I've helped people through the recitation of the Sinner's Prayer and.... there was something momentous happening at that moment. It felt, in the spiritual sense, that a line was crossed, that something fundamental had changed, that angels rejoiced and heaven sang.
Am I delusional? What does it mean to be saved? What is our Good News? What is our version of the Sinner's Prayer?
An evangelist might present the gospel and then ask for people to respond. People go up the front and pray the sinners prayer. They say that's the moment when they crossed the line. But didn't God just save them through Christ's word of the gospel which they just heard, rather than through their response of prayer.
The question is: When are people born again - when they hear the gospel of Jesus or when they say the sinners prayer? Who said the sinners prayer was even necessary for salvation?
According to St. Paul, the word of Christ comes to people through someones preaching and gives them faith. Hence, they confess that 'Jesus is Lord' and believe that God raised Jesus from the dead and are saved.
'The Sinners Prayer' can somehow activate in us what the Holy Spirit has already done. From my studies in church history I conclude that the sinners prayer in the early church was baptism. So after somebody believed, they responded. Maybe that's why it helps people to seal their faith with a prayer.