I dont actually think there's much of a reason behind it? I feel like Akutami, and by extension, Inumaki, just randomly chose onigiri ingredients. From what we know of Inumaki, he has no qualms against stealing the skirt of a classmate to wear as a joke, so maybe Akutami will say that he exclusively speaks in onigiri ingredients as a joke. Except then it gradually evolved into a legitimate thing that he decided to keep using? That's the most plausible idea I can think of.
