“Harry beats Voldemort because he has the allegiance of the Elder Wand because he disarmed Malfoy who had disarmed Dumbledore. However, Harry didn’t win the Elder Wand from Malfoy; it was just Malfoy’s regular wand. So why would Harry have the allegiance of the Elder Wand?”
But Harry did win the Elder Wand by definition when he disarmed Malfoy. You don’t need to physically take possession of the wand in order to win its allegiance. In fact, stealing the wand won’t make it work for you, hence Dumbledore’s plan to let the wand die with him. Remember, Voldemort thought he could just take the wand from Dumbledore’s tomb and it would obey him. But in fact, if Dumbledore had not been disarmed before he died, the wand would not have been loyal to Voldemort just because he seized it. It would have acted like an ordinary wand.