Who knew "the wand chooses the wizard" would be forgotten so quickly that people start calling it a plothole when a wand chooses its wizard.

I forgot about that.

Maybe. If that's so, Harry should have snapped / burnt the Elder Wand if he really wants its power to end.

Harry did break it in the final movie (but not in the book). Therefore that should have removed any power it had (had least in the movie)

Yeah different woods and core combinations have different properties, like I think dragon heart string values the duel thing more than others, and maybe elder amplifies something like that? Just a thought.