Could Bruce honestly ever be the White Knight in the eyes of Gotham though?
Yes. 100% You have two and a half films leading up to it.
Taking off a mask does not a white knight make. His methods were always extreme, illegal and dangerous. It just wouldn't suit him. Bruce circa BB and TDK wanted more people like Rachel and Dent working WITHIN the system, fighting corruption legally.
But TDKR through out all the rules. Suddenly you have Batman willing to kill to save Gotham. You have a city that has lost it's laws in place of chaos.
"One day the Batman will have to answer for his crimes..." -Harvey Dent.
Indeed so but that's apart of growing up isn't it? When Batman takes the blame for Harvey in TDK, for me, that was the most heroic thing I've ever seen a superhero do in a film. In that moment it wasn't about him, it was about saving Gotham from what Joker had done.
The system fell apart in TDKR, the best way to save it was to restart it. Bane had complete control over Gotham. It would have been nice if the people of Gotham finally stood up for themselves (as Bruce original intended Batman to inspire) and take their city back from Bane and who better to lead them than Bruce Wayne.
Does he have to out himself? No. It's not necessary, I'm saying Wayne needed to be the figure that Gothamites strived for and the movie hints that that's the ultimate goal. When Blake scolds Bruce for the funding of the Orphanage...that's IT! That's the kind of way Wayne could influence the city. When Alfred suggest Bruce give his information to the police...that's it! That's the way wayne could influence the city. They needn't know he's Batman, the simply needed to see that Wayne had grown up and would use his incredible wealth and power to protect the city. Additionally when something came up that needed a more...personal approach...they had Batman.
This is how it's been done in almost EVERY other Batman mythos. Batman fights the criminals. Bruce patches up the city so that it may have it's advantages against them. He could have been the face people looked at during Bane's siege and inspired them to not give in to Bane but to fight for their city. The same way Thomas and Harvey inspired them.
TDKR goes right back to the beginning and explores the meaning of what the bat symbol was intended for in the first place. It's about reaffirming the value of that symbol. Sometimes they are more powerful than men can ever be, I think that is one of the whole points of the trilogy.
But Wayne was a symbol already. Batman was a way for him to be something to the criminals but he hadn't figured out how to be something for the people. Time and time again we are shown that while Batman is good at fighting crime he still hadn't inspired the city the way he wanted to. When Bruce talks to Alfred about the copy cats he says: "When I said I wanted to inspire people this is not what I had in mind" all he created in them was more vigilantism and violence.
Then at the end of TDK Batman must become a wanted criminal to protect the image of Harvey Dent... not the other way around. Dent's purpose in Gotham was always more important than Batman. The trilogy NEVER EVER suggest that these symbols are, in fact, stronger than the actual person. Sure Bruce says it in BB: "As a man I'm flesh and blood but as a symbol..."
I know that.
But the one consistent thing about BB and TDK is that Bruce is almost always WRONG about things. He is in a constant state of learning about the world about. Ra's readily admits that Thomas was how the league was beaten the first time. Rachel tells him that he isn't Wayne but in fact Batman, that that boy never came back.
Even Bruce is inspired by Harvey Dent in TDK. It is the actions of men who are visible that shape Gotham. Thomas, Harvey, Gordon... not those who hide in the shadows. The trilogy has always shown that.
Batman was a means to curb crime and halt corruption but it would have been impossible with Gordon, Harvey and Rachel. People who put their lives on the line by being public and thus showing Gotham that there were other Gothamites who weren't afraid of the crime.
TDKR's first half hints that perhaps this is where Bruce needs to go with his life. That maybe Batman has ran it's course and it's time for Wayne to step up but what we see is that we still need Batman, to some degree to physically fight Bane.
But what about the broken city? How much more do you think Gotham would have been inspired if it's richest most powerful came down out of his tower and sided with the people? All that distrust and anger at the powerful could have been undone. Just because they survived a nuke doesn't mean the real conflict was ever addressed. Remember the people revolted against the establishment of Gotham because they saw it unfair. Nolan and co missed a perfect chance to have Bruce combat that rift in the city whilst Batman combatted the physical threat.