Well, i´m glad last year you had The Avengers to entertain you. Much easier to understand.
If you don´t, i´d just to give everyone a glimpse of how bad your understanding about the character is:
You´re right. Batman shouldn´t care only about the big fish, who are actually responsible for most of the smaller fish existence. He should spend day and night catching all the criminals of a city with 10+ million people. Gotham shouldn´t even need a police. Batman takes care of everything. A kid painting a wall? Batman takes care of it.
How about SWAT Teams? Shouldn´t they be writing traffic tickets?
It swings both ways: on the one hand, what drove this Batman, in this universe, to become active, was the organized crime and the effects it had on the city's crime in general; and it was established as early as in part 2 that he generally believed in "democracy" and was only willing to do what he did as long as the system was still dysfunctional.
Once the bigger fish was gone, and the economy improved I guess (maybe a bit thanks to his help in the aftermath), his retirement was consistent with his character, as well as with his growing frustration with the lines he had to cross in the process... of dealing with the big fish - it wasn't the happy retirement he had wished for (and thus set up as his character trait) in DK, but apart from that still more or less the retirement he had been planning to go into (or was it!).
On the other hand, robberies like the Joe Chill one always happen even without three mafias running a town, because the police, no matter how diligent and functional, isn't always there for prevention/justice - and it wouldn't at all be illogical for *a* Batman (not necessarily the Nolan one) to keep going regardless with that as his primary motivation. And that's where the problem with your frivolous, strawman-filled comment comes in - unless you're a firm believer in the system / "no man should have so much power" principle, there's really no particular reason why you SHOULDN'T continue patrolling the streets even with a perfectly functional police at the ready.
No, it's not about beating up jaywalkers and graffiti maestros - it's about preventing assaults, batteries, murders and worse things (mayor's not talking about wallpainters in his opening speech, you know), and doing his part in this in ADDITION to the police, rather than instead of them. Also, not hunting 1000 of them at once for goodness' sake - just intervening as much as he could, intimidating the rest through (you guessed it) fear... which is exactly what you see happening in TDK's opening montage
Plus he's got no jurismydiction to worry about, and can get away with hacking apart way more poisoned trees than Dirty Harry ever could - and... he's got his superior equipment and technology that he doesn't trust the police with... as established in this very movie, TDKR... WHILE its plot is already running!
So this (new - possibly inspired by the sonar thing in addition to the bomb thing) character trait of his, not trusting the already cleaned up police force, can easily work as a counterbalance to his previous retirement aspirations.
He's sitting there in his cave... still not trusting the cops... hiding precious tools from them... that he could totally use to aid crime prevention, but instead he's sitting in his basement/attic and mopes around in clinical, self-neglecting depression.
Hey, could it be that maybe... he really gave up due to said depression, and not because he thought the naughty wall painters weren't worth the effort? Interpretation!!
And that brings us right back to the problems with this film - one of those, if not the central one every other is dripping and sliding down the hill from, being Bruce's retirement. However,
not because "Batman would never give up, man" as that possibility had clearly been set up previously... but because it hadn't been set up previously.
Not this kind of retirement - the depressed, meaningless one, the motivations for which clearly came about way after the TDK credits rolled. The failed energy project, the war wounds that came out of ****ing nowhere. The premature retirement, accepted long before the system became good enough for Bruce to declare that the city didn't "need Batman" now (=in his mind; if it actually
was good enough, he might be overcautious, and be guilty of exactly the kind of flaw some people here claim he'd be guilty of if he were continuing stalking the streets; but we're just talking about character motivations here).
Last movie he did talk about leaving, yes - but that's not how the movie ended; while it isn't clearly stated whether the Joker's chaos or Dent's death changed his attitude regarding this issue or not, the tone of that ending montage DEFINITELY spelled something totally different from "goes into sad retirement". Energetic, action packed, darkly optimistic - things still aren't fixed, streets probably need cleaning up, and the police hunting down Batman with evil dogs; and yet he'll be there, the outcast, hated by the population, but still doing what needs to be done.
Who wasn't pumped to see some of that, if not a whole delicious bunch, carried over into the sequel? But no - apparently, a few weeks later,
real life intervened, as it does, that enthusiastic fever slowly wayned once Bruce returned back home, realized there was kind of nothing to do really, and depression / daily life (and then depression) took over.
Unrealistic? Certainly not. But this is me filling in the gaps that the movie shouldn't just have filled, but filled up with some good, effective "show don't tell" storytelling and character development, not just kinda thrown at the wall to make the new arc work.
Now, suddenly, Batman is old and weak, and has to "rise up" again - not from the exile so tastily set up in TDK (that one is treated very marginally thoughout the whole movie), but from this new plot device that apparently developed off-screen. Chances are he only loses to Bane for that reason, and not because this scary guy is a force of furious nature menace who's risen from hell (he hasn't), and whose drive and determination trump even Batman's (the best apprentice of Ra's al Ghul!!), enabling him to easily challenge the previously invincible super-apprentice of Ra's al Ghul (just roll with it, it's from the first movie).
You see his speed... his ferocity... comes from the same place as the superhuman strength Bruce was able to develop; the ancient conspiracy society (again, just roll with it) who has learned to use a combination of mental, psychobabbelogical drive and secret techniques, moullded by time and success, in order to make its members excel at combat, strategy and stealth to a degree possibly unmatched by anyone else in the world - and he's been born in darkness to boot! Surely Bat's no match for that... so he needs to fall again, and find new, previously undiscovered strenght in himself, in the same dark place where Bane gained his, in order to rise up to his level, and find a yet even new source of will and vigor in order to finally do the impossible and defeat this demonbear of a man (in video game terms: LoS training = better than everyone, + strong personal motivation = best of the LoS, + moulded by darkness = Bane, + ticking bomb or whatever = TDKR!!) and save Gotham from its darkest day yet... oh wait, he's just old and weakened, and only has to rediscover his survival instincts (which he lost off-screen), in order to do that.
Oops! Apparently, this retirement atrocity doesn't only let down the 2nd movie, but also kinda ruins the impact of its own central conflict... feel the drama and excitement slowly oozing out of your soul yet?
It was stuff like this, along with Alfred's sudden concern for his safety (extending beyond the singular threat of Bane apparently) and reluctance to support him, resulting in their extremely poorly set up fallout, the ending twist doing as much damage to the main plot and Bane's character as it kinda gave it all a new interesting angle, the lazy-feeling "rookie cop takes on an elite ninja's job, uplifting music" conclusion, the phoned-in, again hardly set up not-threeway-romance and, not to forget, a whole bunch of awkward line delivery and hackneyed plot devices such as the "clean slate" that made it an inferior sequel to TDK.
Not worthy of hate by any means, very well-made in general as well as engaging and entertaining (mostly), it was just simply a disappointing, inferior follow-up with some weak, alieanating story decisions - probably in need of a rewrite / retool or two.
Yes, just my opinion obviously, but let's do a thought experiment here - let's imagine the movie HAD been rewritten, rectifying the rough bulk of problems I just rattled down, and making it flow naturally from TDK in really exciting ways (feel free to fill in the blanks here), and the real final version would've been released as an early draft that you could read.
Would you go "aww, what a shame they didn't stay with that one", or would you just kinda acknowledge it with a "yea, still cool, but certainly no TDKR!"? Rounding it off with a quip about how this is the devill while that was practice, maybe?
I kinda strongly feel it'd be the latter - but then again, I'm just some dude.
((Edit: cleaned up sloppy language, and cleared up a few points while at it))