However, this is all fixed by TDKR. The Dent Act worked, Gordon's commissioner, corruption and crime are low. So the LOS' plan makes NO SENSE. They're destroying a city that's already been saved! It makes them look like Ras' justification in BB was all just a bunch of b.s., and really he was just leader of a bunch of nihilistic terrorists, but wanted to delude himself into thinking he had a cause.
Oh, and no, the LOS wasn't doing it because the Dent Act was built on a lie. Bane didn't know that until he found Gordon's speech.
I don't think Bane and Talia gave a crap about why Ras was trying to destroy Gotham, just that he was.