we need to remember that the wand chooses the wizard. it is so hard to find just the right one. so to go to ollivander and find 3, just incase they all happen to be fighting dark wizards would be ridiculous.
PLUS the point is to beat your opponent and win their wand in a battle, otherwise borrow one...
this situation would be unlike for most wizards.. we happen to know the only ones would ever be in this situation