PLEASE NOTE THAT THIS IDEA ONLY WORKS IN THE FILM ADAPTATION OF HARRY POTTER

So... Lord Voldemort was obsessed with getting the Elder Wand because he couldn't fatally wound Harry Potter with his own wand, due to their Twin Cores. However, Harry's wand was destroyed in his and Hermoine Granger's fight with Nagini, where Hermoine casts The Blasting Curse at Nagini. Afterwards, when they are captured by Snatchers and taken to Malfoy Manor, Harry gets a hold of Draco Malfoy's wand, and takes it to Garrick Ollivander. Mr. Ollivander says that Draco's wand has changed alligence, and it is now Harry's wand, if he wishes it to be. Harry continues to use this wand, even during the Battle of Hogwarts. Therefore, Voldemort never needed the Elder Wand, and could have probably won the duel between him and Harry, if he had used the Yew and Phoenix Feather wand that chose him, because Harry didn't have his own wand, and Voldemort would have no problems with Priori Incantatem, or inficting fatal wounds on him. What do you think?