1 - the Riddler really could still be a villain and steal stuff, etc. but....yeah, he'd be like a super-mobster; like, The Joker isn't really a mobster....turns out he hates the mob just as much as Batman; he's just a sociopath and hates "Order". The Riddler wants "Order" and "Plans"; he's intelligent and really educated; I don't see him wanting to destroy "civilization"...who would understand his poetry-ladden riddles?
2 - or, you could make it that there's yet another "new D.A." or "new FBI task force leader" or whatever (Gordon is already Commissioner).....or maybe, just the head of their crime lab..............but the point is, he *engineers* "The Riddler" as an alternate persona to get more power. By day, he's mayor/FBI crimes guy here to clamp down on the city and restore order, but by night, he's The Riddler...intentionally starting the chaos that is then used as justification for even further lockdowns. I don't know if that would work though.
But it would be sort of a techno-thriller thing: you know like "Enemy of the State"; the Riddler would be so "smart" that he's hacked the city's new CCTV surveilance system and has taps on all the phones, controls the traffic lights, etc. and he manipulates the city like a giant chessboard. And Batman's got to fight him even though he pretty much controls everything.
Yeah the Riddler's a criminal....but he's not in it for the money: he's in it because he feels slighted by a world that doesn't recognize how smart he is. I'm going by Batman Animated Series, but I liked that whole origin (followed in several spinoffs) that he's a brilliant scientist/programmer whose own company higher-ups fired him after taking him for granted, with a whole "if you're so smart, why aren't you rich?" mentality:
The Riddler doesn't steal because he likes stealing. That would be too simplistic. The Riddler is trying to aggressively prove to the world how smart he really is, and stealing things is just a powerful symbol of that he uses (people notice more when you rob a bank). And in that way he's really narcissistic; that "Psychology of Batman" special said how he's really like Ted Bundy because they both feel compelled to leave clues at crime scenes and taunt the police, and when Bundy was on trial he was gloating about what he did.
So the Joker was Chaos and how the bad "lowlifes" of the mob in Gotham really almost brought everything down.
Well, the "logical progression" is: what is going to be the reaction from the "good citizens of gotham"? the people that "believe in order"?
the way I see it, the Nolan-Riddler would be like, a scientist or computer programmer guy who loses everything because of how rampant the mob in Gotham had become (possibly due to some of Joker's actions in TDK), and he just *snaps*....
....*snaps*, and says "the Joker's whole thing was "plans are useless" and "intelligent civilized people can't accomplish anything, the forces of chaos will bring you down!".........so the Riddler *snaps*, and goes "Oh yeah?!" and basically hacks the entire Gotham telecommunications and surveillance grid, and uses it to utterly destroy the mob more than Batman ever did.......because the Riddler isn't above killing them.
But he's selfish about it, he wants to prove "I did it! and YOU lost!" so he of course, steals things from both the mob and the city to show that "I am in control"......and the Riddles and stuff are things to show how smart he is and taunt the mob and police for not being on his intellectual level.
Sort of like.....remember that episode of the X-Files where a sentient computer kills its creator, who is hiding in a diner, by calling up two rival street gangs? Using satellite and CCTV surveillance it figures out where its creator is, then calls up each of the rival gangs individually and tells each that the other is having a meeting in the diner; both groups barge in shooting and then its creator gets killed in the crossfire.
Things like that; cyber-warfare and stuff to *smash* the mob, but he's also against the police as inherently incompetent, and basically wants to rule as a technocrat. So Batman has to stop him.
But of course he's insulted that 1- as smart as he is, he can't figure out who Batman is, and 2- Batman is, if not AS smart as him, nearly as smart as him. The combined effect leads him to become obsessed with him.