Explain to me how you think it would be a sacrifice if Jesus were only a human versus Him being fully human and fully God. Since you have already said it has nothing to do with ceasing to exist, I'm not getting what you think sacrifice would be.
If you are God and you choose to take on a human form, and then you choose to die knowing that you will still live on — there is no sacrifice. You can say it is symbolic of our spirit living on, but it is not a sacrifice. God can keep coming back in human form endlessly should he so choose. We cannot. Neither can Jesus, if we are to believe there was a sacrifice involved.
If you are the Son of God and you are human, and you allow fate to be fulfilled by dying on the cross — then there is sacrifice. For the story to make any sense at all, and for the sacrifice to have any point, Jesus has to be human.