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I suspect that Nighteye would still have done his very methodical search for a suitable candidate, maybe going with some young police recruit or someone with a similar background rather than trusting All Might's gut pick of Izuku. Also, remember that the initial conflict was born from All Might refusing to rest because finding a successor would take too long. Looking for a suitable person without a quirk would probably take even longer. So I think that the initial split at least would still occur
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Or maybe they feel that they accomplished the least out of all of the inheritors and don't really have any wisdom or knowledge they think is worth imparting to Izuku and are ashamed of that. It's also possible that they used the power for less noble deeds and don't feel like they belong with the others who are proper heroes. There are a lot of possibilities and I'm not sure which one I like the most.
I'm also super-excited for Banjo's anime appearance and to hear what voice he's given in both sub and dub. It's impossible but part of me wants him to be voiced by Ron Perlman since he resembles Hellboy in appearance.
Even Gigantomachia is affected by having multiple quirks I'd say. His endurance allows his body to keep going strong, but his mind is clearly not all there. Though even that is a bit of mixed bag since he can function as a kind of cunning death machine but he's also a simple obedient attack dog who basically needs somebody to direct him for him to function properly.
There are a number of way of seeing Shigaraki at this point. He's a dangerous villain who's committed murder and societal upheaval on a massive scale and absolutely needs to face consequences for all of that. But he's also a victim of different kinds of abuse and failures on society's part, and he got dragged into this same war as Izuku only without giving any consent to wanting to be a part of it. "Do what you think is right." might be the best option and they have to determine what is right as they go along.
You forget one great candidate. KNUCKLE DUSTER!!!! ...assuming he's still alive at this point in history.