Why does that mean that rogues can reach levels of competency in Arcana no wizard ever could? How does that follow?
Because being a master of any skill means being a master of any skill, and while wizards are masters of spells they are focused on being magic users and not ultimate mundane skill mastery, even in the related knowledge mundane skill.
I feel the normal 5e situation of wizards have int as their primary class stat and arcana as on their skill list covers their stereotypical high levels of arcana competence while giving rogues the edge in their chosen skills, but not giving rogues arcana as a class skill or int as a general primary stat covers the general archetypes while allowing rogues more flexibility in their skills concept than they previously had.
This seems to be backed up by the 5e class descriptions in the PH.
"Rogues devote as much effort to mastering the use of a variety of skills as they do to perfecting their combat abilities, giving them a broad expertise that few other characters can match."
"Wizards are supreme magic-users, defined and united as a class by the spells they cast."
Even the section for wizards titled scholars of the arcane is all about the wizards' use of spells.
SCHOLARS OF THE ARCANE
Wild and enigmatic, varied in form and function, the power of magic draws students who seek to master its mysteries. Some aspire to become like the gods, shaping reality itself. Though the casting of a typical spell requires merely the utterance of a few strange words, fleeting gestures, and sometimes a pinch or clump of exotic materials, these surface components barely hint at the expertise attained after years of apprenticeship and countless hours of study.
Wizards live and die by their spells. Everything else is secondary. They learn new spells as they experiment and grow in experience. They can also learn them from other wizards, from ancient tomes or inscriptions, and from ancient creatures (such as the fey) that are steeped in magic.
It is a specific design choice to allow rogues and bards to have skill expertise in any skill and to give wizards a reinforcing double basis for good arcana checks easily (stat and class skill), but not expertise. It does allow the skill classes to be more flexible skill masters in a D&D game where everyone has a decent number of skills (minimum of four compared to the minimum of one in 3e) in a bound accuracy environment.
It makes enough sense to me and I think it works fairly well in the 5e context.
Other setups are viable too and could lead to different theoretical builds and class upper limits for different potential flavor. You could easily house rule to restrict rogues to expertise in their class skills, or grant wizards expertise in arcana, or allow a feat to grant expertise for the cost of a feat.
