Re: Why did the League of Shadows want to destroy a peaceful city?
Honestly, I don't think there was a deep ideal to this plot like their was with Ras' plan.
Ras wanted to destroy the city because he felt the corruption was beyond saving. He failed.
IMO, in Talia's mind, she just wanted to finish what he father couldn't. She didn't see the same ideals that Ras had. She just saw him fail for the first time, blamed Batman for his death and simply wanted to kill Bruce Wayne, physically and emotionally, and destroy Gotham to, in HER eyes, finish her father's work. While that would finish her father's failed mission, I don't think she saw his ideals. She was doing it for the wrong reasons.
Bane was just a pawn in the end. His only motivation was a personal feeling that Bruce betrayed the LOS. And when you consider Bane was exiled, while Bruce was seen as the perfect successor to lead the LOS, Bane was simply jealous. He worked with Talia on her plan, while trying to seek revenge based on his personal jealousy of Bruce and his Ras' view of him. Ras saw Bruce as having the tools to lead the LOS, which he never saw in Bane. I think it's quite simple.
Also remember that, because of the changes in those ideals, this wasn't the same LOS. Sure it kept the name, but without Ras leading it, the philosophies and operations have changed. Compare it to Wayne Enterprises. When Tom and Martha were killed and WE was run by the board, their operations were very very different. They basically set aside everything the Wayne's stood for, and openly said it. Remember the company deciding to go public? It wasn't until Bruce bought the majority share and essentially controlled the company again that he could get his family's name back to what it was.
Change in leadership changes the entire company. The company I work for is going through that, Apple has gone through that, Disney went through it.... it happens everywhere. If you ask me, the LOS' mentality got very clouded after Ras' death and became driven by revenge and personal gain rather than ideology, even if the ideology involved mass murder.