What would Harry Potter have done if the Elder Wand could not repair his first wand of holly and phoenix feather?
Harry would probably have just gone forward using the hawthorn and unicorn tail-hair wand that he wrested from Draco Malfoy at Malfoy Manor when they escaped the clutches of Bellatrix Lestrange and Fenrir Greyback.
Harry looked down at the hawthorn wand that had once belonged to Draco Malfoy. He had been surprised, but pleased to discover that it worked for him at least as well as Hermione’s had done. Harry Potter and the Deathly Hallows — J.K. Rowling
It’s interesting that Hermione’s wand worked well for Harry, considering he had never disarmed her, and also considering the blackthorn wand that Ron stole from a Snatcher never worked very well for Harry, presumably because Harry didn’t win that wand, Ron did.
Ditto for Hermione and Bellatrix Lestrange’s walnut and dragon heartstring wand not working for Ms. Granger.
Still, I’m not sure any of that flies in the face of what Garrick Ollivander told Harry Potter about winning a wand’s allegiance.
I suspect there are softer ways to obtain a (non-Elder) wand’s loyalty, perhaps to just be the close friend of the current owner. Harry had Hermione’s loyalty, after all, so her wand probably just followed suit.
That’s conjecture, sure, but it makes sense in a non-violent, independent-wand-minded, sort of way, especially when we’re discussing Hermione specifically, and the fact that Mr. Ollivander stated repeatedly that he didn’t know everything there was to be learned about wand-lore.
So, I don’t see Hermione’s wand working for Harry as a plot hole, as much as it’s an appealing nuance of the deep inner workings of wand magic to which even Mr. Ollivander is not completely privy.
But I do think Harry should have also won the allegiance of Peter Pettigrew’s chestnut and dragon heartstring wand, and Bellatrix’s wand, considering both were in Draco’s possession when Harry grabbed Draco’s wand.
Ron had disarmed Wormtail first, then disarmed Bellatrix of her wand, only to immediately turn around and give up both wands to Draco after Bellatrix Lestrange held a knife to Hermione’s throat.
So I don’t know if Wormtail’s wand should have answered to Ron, as Mr. Ollivander suggested it should. There’s our plot hole. I knew Rowling wouldn’t let me down.
But, to complete the question, had the Elder Wand not repaired his old wand, Harry could have simply retained the Wand of Destiny as his own, although I think he still would have wanted to return it to Professor Dumbledore’s crypt to reside with his old mentor forevermore.
At least in the interim, Harry would have continued using Draco’s wand until he had Mr. Ollivander fashion him a new one or he just decided to keep the wand of his old nemesis from that point forward.