What Does "Come Into My Heart" Mean Anyway?

The church norm for the past 20+ years has been to have an "altar call" at the end of services where non-believers are asked to raise their hands if they want to "accept Christ." If they raise their hands, they are led in a call-and-response prayer where they copy the Pastor's lead to "ask Jesus to come into their hearts."  

Many people consider this a pivotal part of the service and get frustrated if the Pastor doesn't include this in every gathering. The number of people who raise their hands gets promoted; everyone considers it a great service if many people raise their hands. The success of the pastor or service is quantified by how many people raise their hands.

This has just been a normal part of my up-bringing and faith, but just recently I took a second look...I considered it instead of just accepting it as a norm. And I'm no longer sure if this is a healthy way to quantify the presence of the Holy Spirit, or the success of a Pastor, or even the salvation of a new believer.

I don't think conversion ususally happens in an instant. I in no way doubt it can, but I don't think it's the norm. I also wonder if saying a simple prayer, that's likely not even genuine or understood because it's just a copy of the Pastor's words, is the gateway to salvation.