The problem with that argument is that the rogue class doesn't actually give proficiency in arcana in the first place. A rogue has to go out of his or her way to add it somehow, and it's not that arcana is not broken down into categories -- arcane magic is broken down. Arcana is just one aspect information that's not even a part of the core class. I can make a wizard who is not proficient in arcana at all, uses just his INT bonus (for a reasonable bonus still) and cast 9th level spells.
To be clear, my in my analogy one is spell casting and one is arcana. They are different things in 5e like those two example are different things in real life.
That rogue who has expertise in arcana is just an Indiana Jones trope (expert knowledge) and it doesn't give him access to bard, warlock, sorcerer, or wizard spell casting. Those two mechanics are independent of each other. The connection you are making is concept fluff, and done by taking proficiency in arcana by the wizard.
In the extremes for the rogue example it's +13 for the rogue and +11 for the wizard in the end, and +5 for either in the beginning. The gap isn't significant enough for the extra investment to consider wizards having some kind of disadvantage here.