Absolutely agreed. The preaching I'm referring to never says "Don't you want to go be with _____ when you die ? or the only way you will ever see ______ again is to be saved." The gospel is preached and an opportunity to come to the altar/mourner's bench/prayer bench/whatever your church calls it is given. The trick is, as we often say in our churches, the opportunity to pray is always available. If a person feels the need to pray, they can do so at any time. If anyone else wishes to pray with them, they are welcome to. We would never limit the time in which a person is allowed to pray to only the last few minutes of the service.
By the way, salzer, there is no saving power or grace in the "altar/mourner's bench/prayer bench/whatever your church calls it." How is it blasphemous to offer sinners a time to repent after hearing the gospel, whether they accept it or not? Sure, Christ fulfilled the Law and replaced the sacrificial altar of the Old covenant. For Christians, the altar is now spiritual, a place where we can present our bodies as a living sacrifice. The bench is just a bench. It represents a place of prayer. A sinner seeking to repent is just as welcome to pray in their seat, or go to the back door and pray, or go to the water fountain.
In your notion of service, how should repentance be handled after a sinner hears the preached word of God?