Bane and Talia were not the LoS. Her whole thing was getting revenge for daddy and making him proud, and Bane went along with it for her and because he liked fukking shyt up. Whether or not Gotham was still corrupt is irrelevant.
well, true and incorrect. bane & talia WERE the LoS! like alfred said, SOMEONE HAD to take over the LoS after the demise of ra's al ghul in which bruce blew off stating bane's merely some lame mercenary
then later on, BANE himself stated that HE WAS THE LoS there to fulfill ra's al ghul's destiny.
they really believed in that sh1t, because him AND talia (as talia stated) were trained by the LoS, and not only that were set to blow up IN gotham along with the rest of the citizens of gotham. talia's talk of "bringing back balance" echos whut ra's been talking about.
so, it's MORE than just making ra's proud...they believed in that sh1t as well. that said, it's an extra caverat to destroy bruce in everyway possible.