There have been a few posts with suggestions to make all stats useful for all classes. The issue with making all stats equally useful remains that people only get X points per level, and encouraging everyone to spread their stats around just produces a party in which everyone has pretty much same stats as every other member despite having different weapons and attack styles.
I have seen games where STR is the only stat for increasing the damage of basic attacks, but those games are typically JRPG's where you don't allocate your stats, they all increase when you level up, and they also have a separate Magic attack stat which governs how powerful your magic attacks are, to differentiate physical attackers from casters.
Your suggested system will produce much more homogeneous characters than the current system.
(Also, this game seems designed around the idea that you have a max of 6 AP and get 4 AP per turn, and you cannot permanently increase either of those numbers.)
Personally, I think Pillars of Eternity, which has a stat system much like the OP's, produced an amazing variety of builds. I mean, it was kind of hilarious how Barbarians could invest in a lot of intelligence to increase the AOE of their physical attacks, but also awesome. When I looked at the forums, I was impressed at how different people built the same classes (though some classes were more pigeon-holed than others).
That said, I'm sure a system where all stats are useful can easily lead to homogeneity if not done right. The key is to make all stats useful, but not essential, to all builds. In general, intelligence should be the best, most important stat for mages, so I don't know if strength should increase magic damage, for example. Any sort of mage damage build would mandate large investment in strength, especially if it also increased vitality. I also think memory should stay as a stat, and wits could probably stay. So I'd probably suggest something like:
Strength: +Physical Damage, +physical armor, +carry weight
Finnese: +Range, +crit multiplier, +dodge
Intellligence: +AOE, +magic damage, +magic armor
Con: +Vitality, chance to resist statuses entirely (like, 1-2% per point), or perhaps only to reduce their duration (though that conflicts with Walk it Off talent).
Memory and Wits as are now.
Range and AOE bonuses are definitely tricky to balance, but I think it's doable. They should be small but still noticeable, like 20% more range/area with large investment.
Perhaps I'd give Strength something like increased chance to set statuses through con resist (like 1% per point). So if Con grants 1% resist per point, and Strength grants 1% resist pierce, than the strength would cancel out a con. But a weak mage might have its statuses resisted (although it probably doesn't make sense to apply this to magic statuses).
I'd also add more physical damage spells, particularly to the Earth tree, that strength would increase the damage of. Possibly it'd be worth nixxing earth damage entirely (after all, what does that even mean?) and replacing all earth damage with physical damage. After all, most earth spells are basically just hitting someone with some form of a rock. I think it'd thematically make sense that earth mages would tend to be stronger than other mages, since they're more about physical presences than the more ethereal aspects of water or fire.
