No. The story is not the problem. It's how it's told and what was missing, that's the problem. And that's what they're adding. The story in its entirety is really, really good. It doesn't need a total reworking. That is absurd. What it needs is more scenes and scenarios depicting things like the Astrals, Luna, and Ravus.
Just putting those scenes in doesn't fix it entirely.
The reason why people say the game needs a rework is because the structure itself is poor, the current structure doesn't really allow exploration of the story much more. You spend most of your time in Lucis, and really, considering how much time you spend in it, not a great deal happens. You infiltrate a base, jared gets wacked and you awaken your power in both weapons and summons. Then you get out of your homeland and the story pacing ramps up, but forgets to show you half of it, or give much gameplay for it (outside of exploring some random quarry and the empire's base).
Don't get me wrong, I don't think Lucis is the problem here, I think that would have been fine as the start of the journey, a decent build up to something more. However, if I didn't already know how many chapters there were in the game going in, I'd have expected Lucis to be a third of the game, not close to three quarters of it.
They'd need to add a lot of gameplay into that final chunk of the game to make it not feel like a rushed mess that was cobbled together because they ran out of time. Which frankly, isn't happening, it's too much work.
It's a shame, because I think the world seemed very interesting, but you literally just see a window glimpse of it.
