We don't know the specifics in making a horcrux. Maybe it required the use of Avada Kedavra? We see that wands can sorta, store their uses in a type of memory when he and harry duel in the grave yard in Goblet of Fire and all of Voldemort's kills pop out as seudo-ghosts. For all we know, that memory is important in the process.
Horcruxes are only made when using the Avada Kedavra spell, iirc. And since Harry's parents were killed with that method, the soul piece went to him.
Also, wands don't store their uses. There is a spell to see the last spell cast.
But, that particular instance caused the souls of the people Voldemort killed to come back. Not necessarily a storage.
By definition a storage. As it stored the knowledge of the kills. Even if it wasn't traditional or a everyfeature. The wand wasn't calling on Voldemort's being for the soul imprint things, because even if he had his old one and it could, Peter killed Cedric so Voldemort wouldn't have had it. That means the wand was the one to have some of them, hence where I got Storage.
Also, wands don't store their uses. There is a spell to see the last spell cast.
But, that particular instance caused the souls of the people Voldemort killed to come back. Not necessarily a storage.