Re: Why did the League of Shadows want to destroy a peaceful city?
I haven't been here for a while, but I will say this on this subject:
Twice Bane says that he is here (in Gotham) to "fulfill Rā's al Ghūl's destiny."
If you read the Batman Begins novelization, Rā's wanted Gotham to serve as an example to the world at large. Gotham in his mind represented the growing decadence and corruption in the modern world, and so as "the League of Shadows (being) a check against human corruption for thousands of years," saw fit to use Gotham as a symbol. Remember, the LOS essentially created the environment that killed Bruce's parents and, in turn, created the Batman, by tampering with Gotham's internal economy, thrusting the city into a polarizing depression.
Talia simply wishes to continue/finish her father's work. So regardless of Gotham's "peacetime," the LOS has a legitimate reason to want to destroy Gotham. But under Bane and Talia, they would have literally destroyed Gotham. Rā's never wanted to destroy the city. He wanted to use Crane's blue poppy-derived fear toxin to let Gotham tear itself apart.
In other words, Rā's was pretty hands-off, Bane/Talia were very hands-on.