I mean we all know doey is canonically a system, a did one at that, maybe osdd, but I really don't know if I, as a did system, can say if he is explicitly bad system rep.
Spoilers for Poppy's playtime chapter 4, Danganronpa 1 and the movie split.
Like i can point to a number of representations in media that are bad. Toko from Danganronpa has a homicidal alter. The monster from split. Split at least showed some of the more realistic representation via showing a little and protector and other alters but lost any good faith interpretation when it spread myths about blind bodies gaining sight from sighted alters and the whole .. the monster thing. Hell I can point to a few ambiguous representations that border good and bad like Sunnydrop and moondrop from Fnaf.
But doey is different. Doey is the enigma, litterally. His systemhood isn't explicitly demonized and his alters arnt the reason he attacks you. Even, Kevin, the "bad alter" dosent cause it. Sure his "bad alter" or the more aggressive one who doesn't listen to authority and throws tantrums has a short fuse but the reason he attacks in the end is because your actions killed the people he wanted to protect and didnt even achieve their goal. To an extent, he's justified.
He's more accurate and harsh system rep in the form of the fact most persecutory alters are meant to be or trying to be protectors in their own special ways. Its his voice, not Mathew's or Jack's, that repeats their mantra and warning, that people who speak gently to them often hurt them. Its a defense mechanism. Mathew and Kevin are both orphans in a facility that experiments on children who got sent there either due to having no where to go or being the children of employees who met similar fates. It wouldn't be a stretch to say Kevin was a victim of our broken foster/adoption system, one wrought with physical, verbal, emotional and sexual violence.
Jack is confused, Mathew is trying to hold things together peacefully and Kevin is just trying to keep everyone safe, including themselves. I don't know if I can see doey, even if he turns into a scary monster who tries to kill you in the end, as bad system representation. Because he's justified. You just litterally blew up the one thing he feels he can do right and feels like he can do to redeem himself. He's justified in attacking you. The visual of three people being trapped in the head of a body just trying to get out as they rip at the seems was viseral as a system. When I imagine my alters within my body, especially to defend it, it's similar. Like your head splitting at the seems like that girl from late night with devil and all these people coming out.
I don't think doey is the most sanitized, clear and easy to digest system representation possible. I know some touchy just-realized-they-were systems in teen bodies and "endogenics" who have no business in this space are gonna cry from the roof tops with zero nuance that because he becomes a monster at the end and dies a sad death, he's bad rep. No if, ands or buts. We aren't talking about a well thought out, barely visible background character in some grifter qUeEr Netflix slop that's all fluff and no hard candy.
But. For what he is, it's... Good? Not great. Not the best *tm. But certainly way above the worst. Way above bad. Although I could argue it could be better and your fair to be on the fence, I think he is. I think he's good rep. He's raw. He's real. He's clear and he's justified. Although we could make arguments day and night about wether or not the team at Poppy's playtime intended for doey to be system representation or not, I think it's pretty clear he was and for being made by a group of people without a (outwardly) system amongst them, it's good rep. He's ok.
I think we finally have one. One who shows it's not a death sentence even if he dies at the end and shows it doesn't make you a monster even if he becomes one. He's no bigger, scarier or more ruthless than any other experiment, not by a long shot and I think that's good. I wish he survived, I wish he didnt turn into a monster. I wish he would of simply escaped but I think he's ok. I see the representation and I raise you, maybe let the next one live to the end but keep up the good work? Its clear from the outside you tried and did a fairly good job. We need more casual rep.
*edit: didn't know the persecutory alter had a name, fixed wording.