Regarding the allegiance of wands:
First of all, upon rereading the excerpts that I quoted from Ollivander, it seems to me that Ollivander wasn’t 100% certain about the idea of wands changing allegiances. Notice how he says things like “then it may be yours”, “I think so”, “I think so”, “Whether it needs to pass by murder,
I do not know”.
Additionally, there could really be two separate issues here. The starting point is that a wand that is not yours doesn’t work well for you. So theoretically, “winning a wand” could just allow it to work well for you without the added chiddush of allegiances changing. Ollivander’s statement of “Yes, if you won it, it is more likely to do your
bidding, and do it well, than another wand” would reflect this. Though Ollivander does seem to hold of the added chiddush.
But getting to yekke2’s question, I think I was sort of alluding to this earlier, namely, that if disarming someone causes a change of allegiance, then there would really be complete anarchy. Wands would be changing allegiances on a daily basis and no one would be able to keep track of it. Also, in the third book Harry disarmed Snape. So Harry should have had the allegiance of Snape’s wand. Now sirvoddmort might answer both of these points by saying that when the person took his wand back, he regained its allegiance.
Stam a kashya – how did Dumbledore defeat Grindelwald if Grindelwald had an unbeatable wand? Unless “unbeatable” is lav davka.