Actually, Jesus did die with a lot of eyes closed. To this day the Jews deny Him as Messiah.
Peter WAS embarrassed and denied that he even knew Jesus. - Mark 14:66-72
Judas hung himself - Matthew 27:5
S/Paul killed Christians and was "trembling and astonished" when he first heard Jesus calling - Acts 9:6
To answer your question:
You've never been busted in a lie and felt embarrassed?
You've never done something and felt bad upon reflection?
You have never sinned and felt bad?
I have willfully sinned and was embarrassed in the situation, and still sinned anyway. To this day, I feel embarrassed that I was so wrong and so rebellious.
The question, during service, and the command to keep our heads bowed, and eyes closed, isn't because Jesus would be ashamed. He already knows what we did. He knew I was gonna sin before He formed the Universe. It's because we are ashamed of our own sin that we close our eyes and bow our heads. We afford that comfort to those that do, in that moment, recognize that they are sinners in need of a Savior.
People don't want to be judged. The thinking here is that if no one is looking, it makes it easier to raise their hand. Kinda' like when you see posters for lost articles that say "Please return, no questions asked"
One isn't saved when they raise their hand, they are saved when they accept Jesus as their Savior.
This usually takes place after the service, when someone opens a Bible with the one who raised their hand. Then, usually the next service, or before the end of the current service, and announcement is made that the person who raised their hand has accepted Jesus as their Savior. They are then welcomed into the family of God.
FTR: I've never seen a pastor in an IBC call the people who raise their hands to come to the alter for salvation. I have, however, seen it in a Pentecostal church.
Usually the alter call is for the saved, born again, Christian. It's usually to repent of something that happened either during the week, or something that was brought to mind during the service's message or both. (1 John 1:9 and Romans 13:11-14)
One is not required to go to the alter to repent, this can be done while standing there, or at home. The idea is to take care of business with the LORD while it's still fresh on your mind and heart.
I hope this was helpful