The skill stat, at least in D:OS EE, lets you learn more skills, and lets you use higher level skills without a penalty to AP-cost. We don't know what will change in D:OS 2, but I don't think cooldown reduction needs to or should be added.
I absolutely do not agree with a cooldown spread of 9-turns at all. Pretty much no skills even have a cooldown of 9-turns, even in vanilla. That's completely ridiculous and would just bring back the exact same skill spamming issue.
Here's why I don't like cooldown reductions:
If you can spam the same skills turn-after-turn-after-turn, it reduces the amount of strategy and tactics. You no longer have to worry "should I use Skill X now, knowing that it means I won't be able to use it again for a few turns?" It means that you no longer have to worry about running out of your best spells and having to figure out what to do with the limited resources you have left. It means scrolls become much less useful.
