While what she can do with it is flexible, when she casts it it is inflexible. Stuck being the last skill she cast. Timing is more important than management on her, and having a cost associated with her ultimate hurt her a lot when it was there.
LeBlanc used to be a very weak pick until she was touched up some part of which was her ultimate being stripped of its cost. At the time, that was really necessary for her to function. You may have a good point that it may no longer be needed for her to compete, as she's pretty strong at the moment. But then you have the question of the amount you tag on to it?
100 mana would be steep, and would heavily affect how often she would be able to use it. If that's the case, her basic skills would have to be more impactful in order to compensate for the loss of usage she gets from her ultimate. Otherwise, she'd be pushed back in to her joke pick state. An amount based on the mimicked skill would be steep as well, as W alone reaches a cost higher then 100 mana. And then your other choice, to go lower, say with a 50 mana cost may not impact her much at all assuming she has something like Lost Chapter/Morellonomicon and the change wouldn't do anything like what you wanted.
Personally, I don't think her ultimate being free to cast is what's making her as strong as she is. I think her prominence at the moment is more about the meta game as a whole, which sort of requires high mobility and high damage from a mid laner, pushing towards champions such as LeBlanc, Ahri, Zed, Yasuo etc. especially when they can reach those values without snowballing (of which LeBlanc is probably the least consistent of those four). I do find her a lot more frustrating to play against than I used to, but her ultimate's availability isn't really what bothers me, it's more her high damage values in laning phase that makes it easy for her to poke and kill pre-6.