I think is coherent. I am a ranger who fights wizards, pretty sure i have to understand how the weave function, wich are the spells used by mages, learn about their uses and battle strategies, understand how to recognize magic traps and so on. That is the dominion covered by the Arcana profiency.
Instead if i am concerned of fighting the devils I likely would study whom they are, what are the differences between the different kind of demons and devils, how to protect myself from them, how to recognize a devil that disguise themselve as some other race. That is I'll probably increase my arcana lore and learn the protection from evil and good spell (I would add the reveal evil and good spell too).
If I am a bounty hunter I'll probably like to know how to follow hints and clues, how to extract information from people by interrogation, I would also try to have connections with the underworld thus learning their code, and probably i would be sure that the target has to struggle to free themseves from my traps and so on.
I get that rpg now are more about built than backgrounds and that DnD specially is influenced by this kind of approach. But not everything that doesn't align with that kind of approach has to be an error or something did in a half assed way, like in this case.
Obviously the attributes the gained skills rely on are not those of the class. But again how many of us rely in every days life only in a single aspect of our abilities?
