Technically, we already have AP in the game, it's just poorly implemented in PvP. It shouldn't be too hard to attach traits to gear and let players work on unlocking them permanently.
All they'd really need to do is give us a new traits window, with the traits functioning slightly differently (functionally the same as Additional Skills for the most part). Lets say I equip Valerian Dragoon's Mail, and that has High Tide on it (which increases the rate the Limit Break meter fills by a balanced amount). High Tide now shows up in the new traits window permanently, however I can only use AP (which would be tied to your level) to have it in effect while I'm wearing the armor it originated from. Alongside the trait though, is something along the lines of 0/100. That would increase through battle as long as I'm using AP to have the stat in effect, and when it reached 100/100, I no longer need Valerian Dragoon's Mail equipped to set AP to activate the trait. I'd have the trait permanently and could do whatever with the armor.
While some of that would be new to implement, I'd much rather have a well polished system like that, than have them continue to shoehorn materia into this game... Keep materia as a regular stats option (and actually work on them meaning a damned thing), I'd rather not go about looking to replace my High Tide materia every time I upgrade gear... I'd love it if they could rework stats in this game to the point where Paladin could benefit from melding Mind, or Dark Knight could benefit from melding Piety, and I'd have no real problem spending Gil to remeld basic stats like that with each upgrade, but actually interesting stats? Either that is a nightmare scenario where I'm frequently looking to obtain more High Tide materia, or I can just take the materia off old gear and put it on new gear, at which point the new materia contributes nothing to the games economy and it becomes more of a chore than anything...
There's also something to be said for losing meld slots with stat bloat... You'd be reducing your chances at specific materia by adding any new form of materia, which I'd consider bad, and you'd also be reducing the chance of "successfully" over melding, since you'd have more options for what stats to meld. You'd have more options of what to meld, sure, but I don't actually think that is necessarily a good thing. I'd rather see materia be my primary and secondary stats, and another system entirely for stats like High Tide. IMO it would be messy to just overload materia with potentially hundreds of additional stat options, I'd rather see two good systems, than one incredibly meh system. Though right now I can't really consider materia to be a good system anyway, maybe if they reintroduced having two main primary stats instead of this incredibly dumbed down system...