I will just correct this misunderstanding. Jesus had to die for the same reason as you believe. There can be no forgiveness of sins without the shedding of blood, regardless of whether or not God chooses. The means of salvation does not change. Jesus died to atone for the sins of those who will be saved. If God predestined some to be saved, that does not negate the need for atonement.
Could we hash this out a bit?
If God chooses who will be saved, there was no need for Jesus to die on that cross.
God always required a sacrifice for the forgiveness of sin, from the Garden and onward.
Why?
Because God is almighty and the sin toward such an almighty being requires a big sacrifice,
in the OT it was animals that had to be slain continuously, and in order to have the one and last sacrifice it had to be a perfect being, a god, because a god was damaged by Adam's sin.
The animals DID have to be sacrificed in the OT as some type of atonement - pick one you like.
And Jesus, both man and God had to be sacrificed in the NT as some type of atonement - pick one you like.
The plan of God, since He knew Adam would fail (Knew NOT predestined as calvinism believes) was to OFFER The Son as an atonement and whoever would believe in Jesus would be a member of the New Covenant and be able to enter into the Kingdom of God, both here on earth now, and also after death in the Kingdom of Heaven.
The kingpin was, of course, belief in Jesus.
He who believes and obeys the Son will have eternal life. John 3:36
In Him was life and the life was the light of men. John 1:4
That which is BORN of the flesh is flesh, and that which is BORN of the spirit is spirit. John 3:6
He who does not believe has been judged already because he has not believed in the Son. John 3:18
Anyone who drinks this water shall never thirst again. John 4:14
You are still UNWILLING to come to Me, that you may have life. John 5:40
The above and many other verses, shows that we must be willing to believe in Jesus in order to be saved.
This is because, through our free will, we choose to believe in Jesus. THIS belief will cause our spirit to be born again through our Lord.
IF God chooses who will be saved, what would be the reason for Jesus to die?
No one has to choose Him. No one has to believe in Him because it's GOD that will choose the saved.
No reason for Jesus to have died.