I've been thinking about that, and have come to the conclusion that the "the wand chooses the wizard" thing could mean a
type of wand. For example, Lily's wand was ten and a quarter inches long, swishy, made of willow. We don't know the core of it. Let's say just for arguement's sake that it had a unicorn tail core.
So Lily goes to school, and in her second year is carrying her wand in her backpack and OOPS the backpack falls down the stairs and her wand snaps. She needs a new wand.
She goes back to Ollivanders. She orders a wand, ten and a quarter inches long, swishy, made of willow with a unicorn tail. It works just as well as her other one did.
The only exception is the fact that the particular phoenix tail feather in Harry's wand was from Fawkes, who provided the tail feather in Voldemort's wand, too. In this particular rare situation, that exact tail feather was important in the Priori Incantatum in GoF. In general, though, any other holly and phoenix feather, eleven inch long wand would work for Harry just as well as the one with Fawkes's tail feather.
About the second-hand wands, I agree with Aberforth that there would be a need for one (wands are pretty expensive, Harry's was seven Galleons, and that's quite a bit to the Weasley family). Wizards can use other people's wands, and if my theory about the compatibility of the wand depending on the type, not the actual wand itself, then it would make more than enough sense to have the second-hand wand shop.
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I liked the idea of a wizarding pawn shop!