So, something that I don't think I've seen being mentioned, and it's something from the last chapter of Bleach and not the one-shot. . . Kazui is a Shinigami. Let me repeat that, but slower: Kazui. Is. A. Shinigami.
This is how Ichigo, even tho he was the son of a Shinigami, became one: stabbed by Rukia's Zanpakuto and given her powers, awakening his own Shinigami powers after being a Konpaku for multiple days straight in a deadly ritual that has the very big possibility of turning someone into a hollow, and then awakening them again when stabbed by a sword infused with a shit ton of Reiatsu.
So this begs the question: How did Kazui become a Shinigami? Was he born with the ability to just become one at will? If so, then how or why?