Walther in my above citation answers your objection: ". . . it is true, of course, that God as such cannot die, but Christ, who is true God, could die since He had assumed human nature, so that Godhead and manhood now form one person in Him. A human being's soul as such can, of course, also not die; yet the "whole" human being, consisting of body and soul, dies, and the soul is indeed most affected thereby. So also the most important thing for us is that the One who died for us is true God. If God had not died for us, then no one would be saved."
Let me add that human mortality never becomes a divine property ("God as such can not die"). In personal union, the divine nature appropriates to itself human mortality (i.e., God is man and this man is God).
The death of a mere man, due to its finite nature, would not atone for the sins of a single person. But, be of good cheer! The Word was made flesh (John 1:14). The death of the man Christ Jesus, God's death, is of infinite worth (John 1:29).
