Every stat should have some impact (positive or negative) on everything, pretty much. The only reason it doesn't is because of the constraints of the tabletop inheritance (the thing has to be manageable for a bunch of smart but drunk friends having fun, so to speak), but there's no excuse not to have fuller simulationist complexity in a videogame. I respect the Pillows systems for at least trying to do that, but as always, finding the right balance between simulationist integrity (which demands complexity) and casual fun (which demands simplification and abstraction) is difficult. Sometimes the latter requires gerrymandering together things that don't really go together in the former sense.
At one time it occurred to me that a good balance might be to have "dual stats" where every stat has a "major" and "minor" impact. For example, high INT would obviously play majorly into Wizardry, as usual, but it should also have a minor impact on something like critical chance, or maybe critical damage (you know the weak spots). Really there should be like 4 or 5 layers to every stat, but two might give a lot more simulationist integrity while still being manageable for the poor player's brain in a fun context.