Yes, it's an idea from FFXI, but it was a well-done idea so I thought it might be able to flesh out in this game as well.
Essentially what Grips do (if you never played XI) is they fill up that un-filled secondary slot to give a small bonus of stats. These grips could slightly increase accuracy, or give you a bit of STR, or even Magic Accuracy for DoM 2-handed weapons. This helps to make 2-hand melee classes more effective and diverse without giving so much of a boost, and also makes 2-handed magic weapons more attractive to DoM players who typically would use a shield instead.
I know some of you are probably saying: "But what about Pugilist?!" - Well, as you know, in this game the Pugilist weapons only take up that single slot as well, so they could use them too (I believe Monks in FFXI couldn't use Grips). What Pugilists could do is get Haste stat (Whenever they add that as a stat) grips to increase their flurry of attacks.
Or as far as future dual-wielding classes go, people might ask "well, what about Thief's?" Well, the answer is simple. Since they get to equip another weapon, they're getting those extra stats. Grips help to make things fair as far as extra stat boosts go.
So:
LNC and MRD would equip "STR+ACC" grips (PUG could too if they wished)
PUG would equip "Haste+%" grips
THM and CON could, if they chose to use two-handed instead of a shield, equip "Magic Acc/Crit+%" grips.
Or other types of stats for more variety!
These would give slightly better bonuses to each, while also not being so much that they would break the game and create imbalance between the classes.
They could be crafted and then turned into materia too, and added to higher level grips in the future. It would help add another piece to the economy.
I'll say it again, this is just an idea, so please just try to contribute, stay cilivized, and please don't start flame wars. I know this isn't FFXI, but I think grips were a cool idea that could help 2-handed classes/weapons become more useful.