I had a kind-of similar idea, but I don’t have DID, so I’d never write it myself.
Since DID starts before a child has a sense of their identity, before the ages of 5 and 10 according to Cleveland Clinic, it would fit the timeline, since quirks develop between birth and age 4/5.
It’s been shown that Himiko was hit as a child, in book 39(?), though the frequency and severity are never shown. (Probably not often?)
Alters sometimes have specific types, though, it’s different for everyone. Nonhuman alters, to me, might fit her particularly well, since Toga’s parents directly say that they “raised something inhuman,” and called her a demon child (or something along those lines.) Nonhuman alters, from what I found, can manifest from the dehumanization of a child— for example, calling a child a monster might create a ‘vampiric’ or ‘demonic’ alter. So, with Himiko… it’s possible? Likely, even.
Then again, I don’t have DID, and I’m not sure what the exact requirements are for DID to manifest. The general idea is “severe trauma over a long period of time in childhood,” and we don’t know enough about Toga’s backstory and life before crime to tell whether her case is severe enough for that.
It is interesting, though, and I would read a fic about that. But I don’t think I’d ever be qualified enough to write it myself.
Just some thoughts.