If Harry needed to die, then the Elder Wand should have done its best to follow Harry’s intentions.
The excerpt below sounds like Harry wishing for his death to be quick. If the Elder Wand is tuned in to Harry's intentions, then it would be trying its best to kill Harry.
Voldemort had raised his wand. His head was still tilted to one side, like a curious child, wondering what would happen if he proceeded. Harry looked back into the red eyes, and wanted it to happen now, quickly, while he could still stand, before he lost control, before he betrayed fear —
He saw the mouth move and a flash of green light, and everything was gone.
— Deathly Hallows, chapter 34 (The Forest Again)
Does this mean that the Wand did try to kill Harry? (To follow Harry and Voldemort’s intent.)