#imagine poor kyle inheriting all this baggage while having zero connection to alan or the corps

[incorrect-green-lantern-quotes]

Alan Scott being a Gotham native adds an interesting angle to Batman not getting along with various Green Lanterns. Like, imagine part of the reason Bruce dislikes Guy and Hal so much is that they just don't measure up to the Green Lantern he grew up on stories of. It doesn't matter that the GL Corps predates Alan by thousands of years and he's only an honorary member of it, to Bruce the title of Green Lantern belongs to the WW2 veteran wearing a collared cape.

On the other hand, if we go with the continuity that Alan retired from being a superhero in the 50s with the rest of the JSA because of the Red Scare, maybe there's an element of resentment there. Alan Scott effectively abandoned Gotham and the city went to shit, which lead to Bruce's parents dying in Crime Alley. At least one of the villains that Batman fights used to be Green Lantern's (Solomon Grundy).

So later on when Hal goes full on villain era and becomes Parallax, it's not just a personal betrayal from someone that Batman considered a friend, it's also reinforcing a subconscious notion that you can't ever count on Green Lanterns, they'll always let you down somehow.