AoE should be fairly useless against bosses, so that is very much the purpose.
That said, having no dmg increase at all might be an issue in terms of endgame scaling.
I guess it could be like Increase AoE radius by a decent amount, and dmg by a small amount.
Like 100 points in Str increases singletarget dmg by 50%, but 100 point in Int only increases AoE dmg by 10%, and AoE radius by 30% for example.
Some AoEs will surely start with a small radius, such as a cleave, or an explosion range on Fireball. It would be totally fine if some AoE builds, like a Blizzard Sorc, would not use Int, exactly because the AoE radius was already large enough for the build. That again offers more diversity imo.
It then serves the same purpose as increased attack speed, or reduced cost. Some builds should not want attack speed, even though it increases dmg, due to making the attacks ressource cost unsustainable to keep going. Or due to having a cooldown that makes the attack speed less relevant. Some builds should not want resource cost reduction, even if the skills they use benefit from it, due to being able to sustain attacks just fine already.
Now, in my description above, presumably most singletarget-focused builds would want Str. I guess if we wanted to create a scenario where that was not the case, str could also increase the resource cost of skills? Giving it a drawback. On the other hand, single-target skills is pretty much always falling behind in A-RPGs, with AoE builds ruling supreme, so I am okay with making it easier/simpler to boost them.
Not to mention, the entire goal with making AoE weaker is that we should not have a whole lot of “Single target builds”, or “AoE builds” in the first place. But rather that most builds have both types of attacks in them. So in that scenario, you might probably still use single target skills, without putting points into Str, due to your build focus being AoE.
While, if the system works as I would like it to, another build could use the exact same skills in a build, but put points into Str instead.
Like a Frostbolt + Blizzard build. One str focused. Another Int focused. Or maybe another Wis focused (if Blizzard counts as dmg over time).
Yeah. Which leads me back to what I started this thread with;
the names should be changed. Not because it really matters, but as you say, some people find it odd to have Str sorceress (in Pillars of Eternity Str is called Might instead, which some people still complain about though).
That is back to being more class based. 90+% of sorceresses would be Int based then.
Whereas most other classes might be mixed.
At least, if it became physical vs. elemental, a lot of sorc skills would need to be changed into dealing physical dmg. Which might also feel odd.
Single-target vs. AoE is a better split imo, since all builds can use both, and hopefully most would, unless AoE is as stupidly balanced as in previous A-RPGs, benefit from having both.
I’d be quite fine with one of the affixes increasing proc chances. That is what ADA did too. (and also what Wolcen does in its attribute system, which is actually one of the better attribute systems around imo, as far as I recall it has Crit chance, Attack speed, Life, Proc Chance)
Initially I had added Proc chance to Dex… but Attack speed already indirectly increases proc chance per time, so it felt redundant.
So either, imo, add proc chance to Wis (not Int imo, again, I fear AoE will already be too strong, it doesn’t need even more incentive), or just have it as a gear affix. Not everything need to be in the attribute system 
Of course, another way to go about this, could be to have most Proc chance bonuses in the skill nodes be tied to one of the affixes.
Like Fireball Upgrade Node:
Fireball burn chance increases from 5% to 10%
200 wisdom: Fireball burn chance increased to 15%