"AFO & Overhaul were evil for no reason!"
A lazy psychoanalysis, because I hate hearing the generalization of This and That character had no reason to be evil.
Warning: Spoilers
AFO: Greed and helplessness
The nature of a person's core personality is heavily influenced by their quirk— refer to Toga Himiko (obsessive), Bakugo Kastuki (explosive), Mirio (Optimistic), Dabi (Passion), Shoto (Integration of extreme).
OP: Wriggle eyebrows at the last part
AFO's power is all consuming, overwhelming and greedy. Which explains why that mf tortures his twin brother even in the uterus. He was born on the streets and this went unchecked, uncontrollable. How was it supposed to be? He wasn't even supposed to have a quirk. Heck, no one even had quirks before him.
You know how a pregnant mother's habits, diet and environment would influence a child? If a mother is a drug addict or an alcoholic, her child would have a disorder of some sort. This is a real-life example:
Fetal Alcohol Spectrum Disorder (FASD) & Neonatal Abstinence Syndrome (NAS)
AFO's mother was a prostitute on the streets and that alone was consistent abuse and trauma. But what led her to be forced on the streets? What happened? Where's her family? And then there's this case of epigenetics. I'm not saying the mama was an alcoholic or a drug addict, I'm meant to question you so you'd question yourself: What do you think happened to the mother?
It was just in his nature to be fueled by greed and his environment fed it's insatiable need for power— because powerlessness meant helplessness, and helplessness is a weakness.
"But Bakugo is explosive yet he still chose heroic path!"
Because of the environment he was raised in, despite his mother's volatility and ideals, his father's passivity (and attention to detail— he works in the fashion industry, doesn't he?) and upbringing. He had strong principles and conviction. Not to mention.. he had a role model: All Might.
All of this also explains his high pride despite unstable self esteem and his tendency to push down the weak.
OVERHAUL: Fear of Imperfection and uncertainty
His quirk... dissembling and assembling. He destroys and rebuilds. It's like a kid who is unhappy with how someone built a sandcastle.. NO, THIS IS NOT CORRECT! and then he rebuilds it as he wishes, correctly.
False sense of control...assuming is only way of building is correct, his only order is correct.
His environment worsened this.
Overhaul was already obsessed with power and control (read: fear of helplessness and uncertainty) by nature, he was abandoned without a stable parental/nurturing figure. This made his early childhood terrifyingly unpredictable as a child and his defense mechanism was to become hyper logical, detached with heavy intellectualization of himself and the world.
Sure, the Yakuza's head found him but he found him at the age when he already developed these defense and coping mechanisms.
If anything, the rigid and strict structure of the Yakuza family only enforced his way of thinking. (And his fear of abandonment. Like a stray cat constantly afraid of being picked up one random day and abandoned on the streets again. He likely chased after approval, always afraid)
It was evident he failed to see the nuances in humanity, this was encouraged in one of the sentences thrown to him when all he desired was for validation from his only parental figure:
"Follow our rules, or leave."
Not only that he was an obsessive kid, he was also an obsessive kid afraid of abandonment at every turn. And that statement alone instills an "All or Nothing" mindset, which explains his tendency to Idealize and Devalue. Black and white thinking is a coping mechanism for extreme stress, a way for the brain to compartmentalize emotions to make it digestible. Unfortunately, this also leads to extremes and obsession.
Overhaul has extreme ideologies that obsessed over his father figure.
His obsessive, controlling nature went unchecked with absolute power in his hands— that was what made him the man he was.
CONCLUSION:
Emotional repression and daddy issues are the actual villain in MHA
refer to my previous psychoanalisis...the point of MHA is to figure out how to stop abuse and how to even prevent it from happening in the first place. I've spot abuse here and how it happened... the way you've figured out how Shigaraki and Dabi could've been saved, at which point could AFO and Overhaul be "saved" from their nature?