I've been mulling over this one for awhile, and now that i've gone through another theory involving him, i find it to be worthy of posting. Just a little something i thought up while wondering about the still-unknown past of good ol' Kugo.
As far as i've learned through some research, this isn't quite a new theory. Still, i've decided to share.
I'm wondering if Ginjo was maybe the result of a Hollow experiment performed by Aizen. We all know Aizen did Hollowfication experiments on Shinigami, but is it reasonable to speculate that he may have done some mild experiments on the side to see what would happen to humans who were exposed to Hollows? Not necessarily Hollowfication, per se; but experiments involving Hollows, nonetheless. (Or, in actuality, they didn't even need to be experiments at all. Maybe just observation and study of normal Hollow behavior. Aizen was deeply dedicated in his research of Hollows, after all.)
This could explain how Ginjo became involved with the Gotei 13. Contacted by Aizen, perhaps?
Aizen monitoring the side effects to Hollow exposure, he observes Ginjo as being born of a woman who was among the victims. After some time, he notices Ginjo's enhanced Reiatsu (and possibly unique power, if Ginjo had acknowledged it by then), and seeks to learn more about this new specimen.
I have more in store to this theory, but for now i'll just drop the basic; i'll share more through discussion. So hopefully i can get a good thread going on here.
I'm not sure Ginjo is this but you make a point about Aizen, he probably would've researched if there were degrees of hollowfication, why a human soul can easily hollowfy and shinigami can't, and what the effects of hollow reiatsu are on living humans which would have led to fullbringers. The biggest point to your argument is that Ginjo was undeniably a shinigami during Aizen's time as a captain and there's no way Aizen would've ignored such an interesting hollow influenced experiment. Ginjo may even have been framed or instigated to any crime he may have committed by Aizen to have a better chance to study his power, I just need more convincing that he actually started as an experiment of Aizen's
Yeah, man. The idea of being framed or instigated by Aizen could be a contributing factor to the whole Ginjo versus the Soul Society issue, about which we still know almost nothing.
And like a wanted to clarify, it may not have actually started as an experiment at all. Maybe just a normal occurrence of Hollow behavior, and Aizen just took note of Ginjo as a result through his own research of Hollows.
Also in terms of this theory, i wonder if Ginjo, once discovered by Aizen and brought closer for further study, could have been the "pre-Ichigo" that Aizen was seeking. Aizen had a lot in store for Ichigo because of his powers, and maybe Aizen saw this in Ginjo at first. And with the time frame of Ginjo's backstory, it could be that once Aizen oversaw the greater potential of Ichigo coming into existence, he just abandoned Ginjo as he no longer had any use for him.