Re: Why did the League of Shadows want to destroy a peaceful city?
I would agree that it's vague, although I just think of TDKR as a film that relies more on symbolism overall to make it's broader points.
In TDK, Batman and Gordon make the decision to "bury" evil and the truth, so in TDKR where a key theme is rising/uprising, we have this festering hatred bubbling beneath the surface of Gotham. The economic disparity of Gotham was dealt with pretty extensively in Batman Begins- it's the whole reason Joe Chill ends up killing the Waynes. So what we have in TDKR is a Gotham where those problems haven't gone away. Only now the upper crust of Gotham is in a self-congratulatory mode, proclaiming this to be "the best of times", hiding behind an oppressive new system that they justify using the face of their fallen white knight.
It's not hard to see why an environment like this would lead all the would-be Joe Chills of Gotham underground to serve Bane's army.
"Now this evil...rising from where we tried to bury it."
That's it in a nutshell. That's the point behind the League's return. Evil rises. As sure as heat (or "fire") rising, evil always resurfaces, and it shoves back harder. This is why there will always be a need for a Batman beyond Bruce Wayne. The beauty of that line is precisely in its vagueness. Gordon is seemingly delirious from morphine, and it's his guilt about the Harvey Dent lie that's really talking there. But he's right in a sense. The past is coming back to haunt both of them, and this especially true for Bruce although neither of them realize it. The League of Shadows in this film embody that idea of the eternal return of evil. In the sense that, yes they are the bad guys from film 1 who have come back with a vengeance, but also in that they infiltrate and exploit the existing ugliness in society and turn it into something even uglier for their own ends (which is very much the kind of evil The Joker represented). It's a culmination of of all the evil we see in the trilogy.