A 3-10 range of cooldown times does not make me like the idea any more than a 1-7 turn range of cooldown times. That skill has to be powerful enough to be worth whatever cooldown time it has.
inital range 3-10 is for all. So you could have 5 for low level skill. Or not so dangerous skill.
You want to add in complicating factors of hefty penalties for not optimizing your build for skill X. That highly promotes min-maxing specialization and kills off any use for hybrid classes. I don't see where you get the the idea that punishing not being a pure specialist opens the doors to new builds.
Idea is, you can splash more. You dont need limit skills by 8 Attribute, becouse the skill cant be used often. e.g. If you splash, you get reliable skills with high cooldown. Now you use 8 attribute as a handbrake to limit skills from other branches. I would rather see cooldown as handbrake.
What happened to this:
All that make a sense.
If something works, lets rebuild it from scratch.
Oh, wait ... .
Its still correct. Add skill level to the cooldown system is an extension of current status. Get noticed that some current skills receves reduced cooldown from high DEX