Shields being independent of a weapon is a legacy of FFXIV version 1.0, where shield use was actually a seperate sub-class called Sentinel (SEN for short), thus you could equip a shield to another class and it would allow you to use that shield (specifically, THM and CNJ could also equip shields, although only GLA had access to SEN's abilities). SEN was eventually scrapped as a specific class, shield use becoming classless, and it's abilities rolled into GLA natively (as long as you equipped a shield), and THM and CNJ (and their Job upgrades that were added to 1.0 in a patch) retained their ability to equip certain shields, and this continues into ARR into the present day.

If SE ever were interested in just making shields a part of GLA/PLD's weapon kit by default, I think they would have made it so from ARR's begininng, so as it stands, I doubt very much SE will ever change this, as it would serve little benefit for a whole lot of potential trouble.