I don't think it matters. Almost every single ability in the game that can't be done at-will has a recharge ability that doesn't connect to the narrative in any meaningful way.It would work.
But I find it a bit too mechanical, and not narratively satisfying. What's the in character explanation of why you can't do it 3 times?
I mean heck, why does resting at all regenerate some magical ability? Why is magic coupled to how comfortable and inactive you are? That's just an arbitrary decision put into the rules with the semblance of some narrative function, but doesn't have an in-world explanation. What is it about magic that requires people to only be able to do some things gently and calmly, but other things not? Can't ride a horse and regenerate your magical power. Why not? What does the The Weave have against you riding a horse? You could sit there on the horse being led at a gentle trot for an hour doing absolutely nothing, but that doesn't allow certain people to regenerate their magical power. Why? We have no idea. And that's just one of many things we could ask as to any sort of "reality" between trying to tie game mechanics and in-world narrative.
This is why I gave up on that a looooooooong time ago. I determined from the beginning that the game mechanics are here expressly for the purpose of playing the game. That's it. And if the game wants to try and tie its mechanics to some sort of narrative and story... okay, fine, but I'm not going to need it make any actual sense. Because none of it ever really does.
We create our characters and their stories because that's what the roleplaying has been designed to do. And we play the game part because the game part is fun. And any connection between the two is merely a happy accident.