My feeling are that if you have a resource bar on a champion, the champion needs to be able to use it effectively.
The champion does use it effectively. It is used as a source of healing and can be used at maximum to provide a major source of true damage. That's very effective. What she doesn't use it as is a resource, but that's nothing new. Neither does Trynd, or Gnar, or Shyv. For all of these champions, their "resource bar" doesn't contain an actual resource, it contains information about a modifier for one of their abilities.
The bar is just a more effective way of presenting information. No problems that I can see.
What your quote says to me is not that the champion isn't using the bar effectively. It says that it is using the bar in a novel way (even if it isn't novel), and the particular usage isn't one you like (although I still am not sure why you don't like it). That's very different.
If riot wants to backload damage, there are more elegant ways of doing so.
I actually really disagree. A lot of the way damage backloading is done as a stacking buff. This is just a more visual way of doing exactly that. It makes the information more readily avalivable by using space that otherwise wouldn't be serving a purpose. It's actually such a good idea that I think they should do it more. Riven's passive is the best opportunity. Show it on her resource bar. It would be a massive design improvement.
I just don't think the fact that she has a resource bar means that she should be designed around it. There is nothing wrong with her just having it to convey information if the rest of the kit works well, and it does. I can't really see an improvement unless we're going to just make her another "more fury = empowered abilities" person, which Renekton and Rengar do alrerady, and which I don't think would really be fun or interesting with the way the rest of her kit plays (particularly given that she has some very low cooldown abilities). Her use for it is fine.
The fury bar just isn't part of the theme. The empowered abilities aren't the main theme either. The theme doesn't need to be shifted towards them.