Why didn't Bane reveal to the public that Bruce Wayne is Batman?

I think this is probably because in the bid that he can convince the people to go against the law that imposed the 'Dent Act' and realize they have "worshipped a false idol" Two-Face, he re-enforces his plea with the letter that Gordon wrote expressing how the true hero was the Batman: -

here is the speech:

"I present to you as the shining example of justice. You have been supplied with a false idol to stop you from tearing down this corrupt city. Let me tell you the truth about Harvey Dent from the words of Gotham's police commissioner James Gordon. The Batman didn't murder Harvey Dent, he saved my boy then took the blame for Harvey's appalling crime so that I could, to my shame, build a lie around this fallen idol. I praised the mad man who tried to murder my own child but I can no longer live with my lie. It is time to trust the people of Gotham with the truth and it is time for me to resign. And do you accept this man's resignation? Do you accept the resignation of all these liars?! Of all the corrupt?!"

Bane cared only to rally Gotham against the system that the lie helped create, i dont think the letter really showed the extend of Batmans involvement in the conspiracy, he simply saved the family, vanished and the police vilified him. Batman in a sense needed to appear a victim for Bane which is fine for him if it helps to promote his false hope, in fact the Batman returning is part of this hope while knowing Batman/Wayne are broken and forgotten in a pit to watch Gotham be ripped apart - that seemed to me all he cared about.