So Overhaul thinks the quirkless are those unaffected by the plague of quirks so wouldnt it make sense he would want one with him or to collect them.
I propose an AU where Overhaul finds Izuku in middle school and asks him to join him and his "family" vowing hed have a life of worship and protection. Izuku finally accepts after the sludge villian almost killing him and having his mental state shattered by all might.
He calls Kai who comes to pick him up and stops him from running to save Bakugo. Kai agrees to help instead stealthily manipulating the ground to help stumble the sludge villian until Kamui woods can get a branch to Bakugo. (Because lets be honest he should be useful against a mostly liquid and fuck all mights angst)
This makes Izuku extremely thankful and cements his place with Overhaul.
He then influences Overhauls decisions down the line such as how to improve the quirk suppression bullets so as not to hurt Eri and suggesting Eraserheads quirk over Eris as quirks could return again as the quirk factor Eri effects re-ages but Eraserheads quirk automatically erases most quirks and could do so permanently with modification.
The whole story changes from here as Aizawa isnt there for USJ but All might is since his time limit didnt get decreased.
Also if Overhaul put some time into researching if samegender couples or male quirkless people can have children no one in the yakuza can blame him cause Izuku is mama Midoriya to Eri/everyone.
