Question for readers (if any)

I started to throw in my head with and idea, that how about Fate had a bigger role on the dice rolling.
Like instead of it being a resource for rerolls, how about it being a resource for the actual dice rolls?
And as usual you'd get a Fate point for rolling doubles.

Let me tell you more about it. At the character creation you'd get to "decide" your Fate attribute as well as the others. But with this new idea fate would be slightly higher then other stats. The game would require little more role-playing and less rolling. And the rolls would actually matter since you'd have to really consider when to roll, since rolls would be a semi-limited resource. You couldnt just roll away for everything. So every roll you'd make, you'd lose one Fate point for it, gaining some from here and there. But when your Fate would come to zero, you could not roll anymore for the rest of the game (or session).

Now this is just an idea or a question for you to tell me what you think about it?
It could even be for another game altogether, who knows about the future.
For now i'm just asking your opinions about the idea