Despite the plot holes, and leaps in logic, it works because it has an emotional core and characters I care about. I love the comics, but this is not the comics, it's not the same characters from the comics and I'm okay with that. This is an Elseworlds Batman, and over 3 films, Nolan gave me a Bruce Wayne and Alfred I care about and want to see succeed and find resolution.
I don't get the complaints about Bale's Bruce Wayne at all. The Bruce Wayne we see in public around other people is a character Bruce is playing. It's "Bruce Wayne" in quotes. That's not the real Bruce Wayne and I don't get what's wrong with the idea that Bruce wanted to make sure that the public never suspected Bruce Wayne as Batman and the best way to do that was to make him a rich guy that could never be mistaken for a man with a conscience or an interest outside his own satisfaction. We see plenty of moments across all three films of the real Bruce, in private, to know that this is a good man, a man who cares about others, but who is scarred physically and emotionally, who has human concerns that drive him, not a Golden Age hero without any frailty or doubt driven by plot but also not a Dark Age Frank Milleresque anti-hero on the edge of losing his humanity.
Whatever failings the plot has, I cared about these characters, and at the end of the day, I loved seeing a Batman arc that ended with him being able to step away from the cowl and live a normal life. I think at least one iteration of Bruce Wayne deserves that peace. It's what his parents would've wanted for him, and at least Nolan was able to give it to him. I can't help but feel that anyone angered by this fact doesn't really care about Bruce or Alfred as characters with emotions, but only cares about the cool battles and ideas and plots and slavish devotion to source material. Yes, Batman can't have superpowers, but Bruce Wayne can put down the cape and cowl. He did it in Batman Beyond, and they made it work. He did it The Dark Knight Returns and that's considered the greatest single Batman graphic novel of all time. Why can't he do it here? This is a Bruce Wayne who recognizes that Batman is bigger than one man, that he's a symbol, and that his real goal is not to prowl the streets stopping muggers, but to inspire others to do the same. He does that, in as big and satisfying a way possible, arguably better than any other single Batman story has ever done, and so – emotionally – he absolutely earns the final shot in TDKR.