Leading a repentant person in some version of “the sinner’s prayer” is a necessary final step in the evangelism process. This person is correct - the person may not be ready to fully surrender. Many people go through several cycles of “I prayed the prayer but I’m still under conviction” only to discover that there are things they have not surrendered yet. If a person has been convicted to seek salvation, the Lord wants them to fully surrender, so the evangelist must lovingly (not coercively) give them that opportunity. Not doing so is a copout.
I doubt there's a person on the planet who has *FULLY * surrendered EVERYTHING.
If that were the case, then nobody would be saved. You set up criteria that God did not establish for salvation.
He requires that we turn to Him and if we are still under conviction of sin, then we deal with that as He reveals it to us but that doesn't mean we are not saved.
What you've presented is a works based salvation where were surrender and surrender and surrender yet again and at some point you will have surrendered enough and then become saved.
God meets us where we are, in our sinful state (While we were yet sinners, Christ died for us) and saves us and then the transformation begins. And never ends.
Many people go through several cycles of praying but still "under conviction" because they don't understand their salvation and their security in it. The enemy is loading guilt on them and they don't see the difference between guilt from the enemy and the lies he tells us about our standing before God, and the conviction of the Holy Spirit.