I agree that they're basically the same thing.
I would honestly prefer it if they didn't add pure damage at all to any ability or weapon, and had more general effects. I disagree with your choice of benefits for the following reasons, though:
Strength giving critical hit damage would make strength the preferred attribute for daggers because of Backstab.
Finesse having a chance to give free AP makes combat extremely random.
I'll agree that the current attributes are a little simple, but I also don't like the suggested fix.
I'm not sure what to do about STR, but another benefit from FIN could be a bonus to dodge. However, the exact number of the dodge might be hard to balance. 0.5 % dodge chance per point capping at 15% (40 total points) might work, but it might be too much on top of all other sources of Dodge bonus. But a 0.33333...% chance of dodge per point (capping at 10%, or 40 total points) might be a little small.
Intelligence giving cooldown reduction would cause it to have breakpoints for individual skill cooldowns "3 turn cooldowns are reduced to 2 at XX Int, and to 1 at XX Int." Etc.
It's pretty hard to balance this properly and making each statistic a valuable choice for their respective archetype, like finesse is for rogues, and Intelligence for wizards. (Critical hit damage to finesse, and cooldown to Intellgence get fairly close, though, as far as examples go)
Yes, because of cooldown reduction, INT was super-powerful in Vanilla D:OS 1. It increased the power of mages, while doing nothing to help physical-damage classes, because mages got to increase their power and reduce their cooldowns with one stat.
Physical classes couldn't get the cooldown reduction without splitting their points, reducing their power.