The thing is, that ability is just too generic. Just ash manipulation? That's not how tite creates Zampakutos.
He does not explicity says it nor he needs to, but Zampakuto are heavily themed on japanese culture. Is Rukia's a generic Ice ability? It is not. Sode no Shirayuki theme is the Yuki-onna. Senbonzakura is not a cool looking cherry blossom themed Zampakuto, is about Yoshitsune Senbonzakura, a theater play, sames a Katen Kyokotsu and the children games they play in Japan, or Hyorinmaru/Gonryomaru, dragon-elemental themed abilities and the believe that dragons control climate.
So, I think you focus too much in the ash part of her hit instead of the cat. Her zampakuto is not an ash zampakuto, is a CAT, that has the power to control ash and hide on it. How is that make sense? Well, a
https://en.wikipedia.org/wiki/Bakeneko can control people remains as puppets. That's why I see her ash not as "nature ash" but human cinders. Is the asociation I can make about all Haineko's concepts, among my obvioussly limited knowledge of japanese culture.
If she can only control human cinders in shikai, a bankai where she can control or destroy peoples bodies from the inside in bankai might be plausible. It's just a theory like everyone's is, that's all, but still I do believe the approach is the right one, trying to think as japanese as possible when trying to figure out a bankai.