Board Thread:Questions and Answers/@comment-46731117-20200826115351/@comment-29325824-20200826122721

An owned Asauchi tends to become a Zanpakutō, which lives and dies with its owner. Since most Shinigami manage to turn their Asauchi into a Zanpakutō (even if they're not yet aware of it), and the Gotei 13 probably tries to recover or destroy any lost ones, I doubt many Arrancar or Fullbringers ever get the chance to test out the theory.

Remember, the sole ownership of Zanpakutō is the Shinigami's biggest advantage against Hollows and Quincy. I highly doubt any of them would ever want to risk it that others can start using them. Hell, retired Shinigami are even forced to give up their Zanpakutō, further showing how paranoid the Gotei 13 is about their weapons.