What are u talking about bro, did you even read the book? Voldemort thought that because Snape killed Dumbeldore that Snape was the true owner of the wand. So that is why Voldemort actually kills Snape, because he is following the same theory you are. However we know that Malfoy was the one who actually disarmed Dumbeldore thus winning the right to be the owner of the wand, as at that point Dumbeldore was defeated. In the Malfoy manner, Harry steals Malfoys wand, again disarming him, transferring the ownership from Malfoy to Harry. So essential Snape was a dead end, and he did not need to die.
At the end of the novel, in the final fight, Harry and Voldemort cast one spell, killing curse and experlimus, Voldemort's killing curse however backfires because the Elder Wand cannot kill its true owner, so Voldemort is killed. Harry then chooses to never use the Elder Wand and to our knowledge dies of natural causes and thus making the Elder Wand useless.