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 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 his growing frustration with the lines he had to cross in the process - only it wasn't the happy retirement he wished for in DK.
On the other hand, robberies like the Joe Chill one always happen even without three mafias running a town, without the police being always there for prevention/justice, and it wouldn't 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 to hunt 1000 of them at once - just intervene as much as he could, and intimidate the rest through (you guessed it) fear... as clearly shown 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 which 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.
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 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 the new big guy in town that finally proves a match to him, after long years of invincibility.
Feel the drama and excitement slowly dripping out of you 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 sequel with some weak, alieanating story choices - 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 devil while that was practice, maybe?
I kinda strongly feel it'd be the latter - but then again, I'm just some dude.