Well...if it helps, the way I see it is that DKR was, at least originally, intended to be a 'possible future' for the then-contemporary Batman...which was the pre-COIE version. So he arguably did evolve into a darker and more unstable individual...albeit one still on a noble path to bring justice to Gotham.
Ultimately, its really just a coincidence that Alfred was retconned into being Bruce's guardian and father figure around the time Batman started moving in a darker direction. But I really don't see a correlation there. From a real-world publishing sense, comics got darker in the 80's, DC got darker, and the Batman franchise in particular exemplified that darker tone and aesthetic. And in-universe, I don't think it matters much who raised Bruce...the kind of things he's gone through in his career as Batman is what damaged him over time. It doesn't necessarily reflect on Alfred's parenting.
Unless you're talking about Bruce becoming Batman in the first place. But again, how much of a say did Alfred really have in that? Bruce leaves home at around 18 and spends the better part of a decade traveling the globe and training to become a vigilante. Hell, in some versions, he basically runs away and is missing, presumed dead. He then returns to Gotham and becomes Batman and yes, Alfred does go along with it, but its not like Alfred has much of a say in the decision.
I mean...what's Alfred supposed to do? Turn Bruce over to the cops before he puts on the cowl? Resign and leave Bruce to his own devices, abandoning the duty of care that he still feels he has towards Bruce?
I like the idea that Alfred agrees to help Bruce at the start of his crusade because a) He genuienly believes that, Gotham being what it is, Bruce can make a difference as the Batman, b) This is a great way for Bruce to channelize the anger and trauma of his parent's murder in a positive direction, and c) If he's part of it, he can make sure that Bruce doesn't get himself killed, or doesn't go off the deep end.
Point c is incidentially my headcanon for how the idea of Robin can be justified in a more 'realistic' context. Simply put, these kids were going to do something reckless anyway...its far better if Bruce is there for them and ensures they take to the streets with proper training and resources than just head out and get themselves killed. Dick would likely have gotten himself killed trying to take down Zucco on his own. Jason was most likely heading towards becoming a street criminal looking at an early grave had Bruce not taken him in. Tim I think would have chosen to be Robin, or some kind of crime-fighter, even had Bruce not accepted him. And Damien...well, being Robin is way better for the kid than being the heir to Ra's al Ghul!