Something I've done recently (and I really like how it plays in practice) is to simply give all characters a single stat for offensive power (PWR), which combines the traditional roles of STR and MAT. This solves a lot of issues (such as making it clearer why a skill is doing high or low damage), but most of all it avoids creating dump stats (such as STR for mages). PWR is used in every damage formula, so if you make the choice to invest in PWR for a character, you are trying to make them a powerful damage-dealer, whether they're a warrior or a mage.
It may sound like this makes melee characters and spellcasters too similar, but I tend to differentiate them in a couple of ways. A warrior-type character is more likely to have a high natural PWR stat, whereas a mage-type character will have lower natural PWR numbers but the multipliers on their skills will be considerably higher - so the Warrior can consistently put out damage with basic attacks and skills, whereas the mage is more about higher spikes with skills but a lower baseline. In one game I also give spellcasters a different battle flow - they start out each battle with lots of stored mana to use spells, but in order to get more they need to spend turns converting TP into mana, whereas melee characters use TP for their skills (starting out with only a little TP but quickly regenerating it throughout the battle). The stats are simple and uniformly useful, so caster weapons can be very similar to melee weapons - but the mechanics for spellcasters feel satisfyingly different.
One other thing I've seen done with caster weapons that I like a lot can be seen in mid-generation and recent Tales Of games. In these Action Battle System games, spellcasters' weapons tend to give similar amounts of STR to melee/ranger characters' weapons (in addition to giving a small boost to MAT), and spellcasters can even have some pretty respectable natural STR stats. The difference is that melee characters tend to have very quick, smooth attack/skill combos, whereas spellcasters' attacks are slower, clunkier, and don't combo into skills as well. This means that if a spellcaster tries to run up to enemies and whack them with their staff, they're probably going to get beat up in the process, making it more of a feasible last resort when being attacked (or when out of MP). They can still put out some good damage with their spellcaster weapons, but the degree of difficulty in doing so is high and they're left open to being mercilessly counterattacked by the enemy (as opposed to when they're far from the action, safely casting spells while the melee characters soak the hits). So while you ideally don't want casters using melee moves too often, their weapons' STR boosts are appealing in that you do get significantly more damage when you do have to use those melee moves. I especially like this system because it means that different characters have unique and appreciably different playstyles, while again avoiding the dreaded dump stats.
