Again, that system literally did not even affect your player level or skills. You simply had access to any and every skill you had unlocked across all classes, limited only in that true ranged attacks couldn't be used by melee weapons (even the inverse wasn't quite true). Technically "cross class" skills weren't even a thing; you just had a total bank of skills and grabbed the from whatever classes you liked. Wanted a party Pugilist tank? You could build that. (It was even largely meta on Ifrit since you could dodge magic but not block or parry it.) Solo pugilist survivalist? Drop some enmity skills for more self heals.
If you were a level 44 with an axe, you'd still be level 44 when you swapped to a bow. Your skill selection and hotbar would swap, and that was all. In the original system, you played a character, yourself, not a class. Swapping to classes of different levels (not merely proficiency ranks) by changing weapons already marked Yoshida's massive change to that original idea.
And let's not pretend that weapon types can't be shared within the current system. Until Heavenward, Gladiator still also used daggers. Both Conjurer and Thaumaturge use wands, canes, and staves. Both SMN and SCH use books. The distinction posed by weapon types is no more significant than the sheer aesthetic distinction one would want between the silhouettes of any two jobs even without (pseudo) class-specific weapon types.
