Eww, 1 day cooldowns? Who actually likes that?
I swear, I've used the eye of fear Kahjiit power twice, and the summon ghost power for the Dunmer once. And and I played on both characters for more than 200 hours...
So no to greater powers, I prefer a cooldown of a few minutes.
little to no cooldown for generic spells? sure. huge stamina/mana cost to cast something powerful? certain death approaches, and there's only one ability that can save you but you shouldn't rely on it all the time so it has a long cooldown? that's fine with me too.
maybe some greater powers can just be passive. but if something is of great power, i think it makes sense if there's a huge cooldown. and since you don't use greater powers, then you don't have to worry about cooldowns.