This is essentially what THM originally was designed as in the beginning of FFXIV 1.0 (it was more about casting debuffs and healing using drain spells) - it was CNJ who was the elemental spellcaster. This changed after Yoshi took over and the classes were redesigned to accommodate the Job upgrades (thus some of CNJ's elemental spells were given to THM to ensure it was a better fit for BLM, losing it's drain healing and debuffs in the process). ACN in ARR essentially gained these debuffs anyway so I don't see SE bringing the old THM idea back sadly. The sole surviving legacy of 1.0 THM left is the astral/umbral shift mechanic - 1.0 THM's spells were entirely astral or umbral aligned.
A certain design document floating around on the net from 1.0's early development actually references (among other things), a special 'Adventurer' class (abbreviation 'SPN') which is bare-handed, presumably what you're describing. I can only speculate why this was never implemented though, probably due to how the Armoury System was designed requires a weapon to be equipped at all times and thus the 'bare-handed' aspect probably would have caused too much issues for it, so they never bothered with it.
As it was 1.0's original (pre-Job) Armoury System was specifically designed to equip any ability on any class, allowing you to mix and match to your heart's content (classes were less 'classes' and more just a weapon with a set of abilities attached to their use). This did not work nearly as well as it did on paper though and ultimately classes gained more rigid roles when Jobs were added to them, thus resulting in the more rigid cross-class ability system that was carried into ARR (and recently removed completely, replaced by the 'role ability' system). So alas, I do not see SE going back to this idea in the future, it's pretty clear they want to keep classes and Jobs within dedicated roles with little variation (because class/ability personalization/variety is a myth - players will inevitably find the best, easiest set up that gives the optimum benefit for the least outlay and so that will become the meta, with every other possibility shunned and players harassed accordingly if they dare "think outside the box." FFXI suffered from this bad, and FFXIV's design is an attempt to at least try to eliminate that. So I do not see this changing I'm afraid.