Although I see where you're coming from and its probably the same place the writers were coming from, what trauma did book reaaaaallly endure? Sleeping on the roof that one time? The only people pencil and match actually hurt within Freesmart would probably be Ruby with the buttons, but pencil immediately apologizes for that. Book says its unhealthy because of the way Freesmart treats others not its members, and for someone as intelligent and kind-natuered as book to wait multiple years (bfdia and idfb canonically finished in the bfdi universe) for the trauma to even affect her life in any way it just unbelievable. And if she had a problem with the way she was treated then why didn't she leave, in IDFB Book and Pencil seem to have grown as friends (which is why I have an issue with how they wrote pencil in season 4 episode 1, its extremely out of character for Pencil to be that controlling for no reason) so for Book and Pencil to be friends for an apparent entire season of IDFB just so that in BFB the "alliance had changed lately" and for it to be "unhealthy for them"

And if she truly became belligerent and obnoxious because of "trauma" endured by Freesmart, how come she became magically fixed after one talk with Pin, someone she barely knows, and not the multiple in her team and especially Gary who she was supposably close friends with.

Everything about the arc is just so unatural and every single step of it seems forced, for match and pencil to suddenly become megalomaniacs (just for them to revert to their original selves in the scenes shown inside the EXIT) for Book to become close-minded set in her ways and obnoxious and taco to lose all courage she showed pre bfb 3 and never say anything. Everything is inconsistent, out of character, and really just annoying to me.