yeah that Riddler one has been floating around (probably fanart)
still, I think Riddler actually would make sense THEMATICALLY, more so than Catwoman:
Batman Begins - Bruce Wayne becomes Batman, having to overcome fear in the process -thus, they use Scarecrow (with a mix of Rha's Al Ghul)
The Dark Knight - "Escalation" - just like The Long Halloween, we see how the "old school" style mobsters start to get superceded by supervillains like The Joker; arguably, because Batman has attracted such a drastic response from the criminals (I don't think Batman "attracted" such crazy super-villains to appear in Gotham....I think what happened is that he made the ground fertile for them; he made the old-style mobsters so desperate that a "new kind of criminal" they felt was needed to rise to meet the challenge of Batman.
So in TDK, Joker represents pure unadulterated Chaos, to Batman's dream of Order. Joker's whole speech to Harvey where he explains that he just "does" things and HATES "Plans" and "Order" of any kind, not just of the police but even the relative "order" that the mobsters used to have under their criminal empire at the start of "Begins": he truly is a sociopath.
But (as opposed to like, Catwoman) Riddler is the opposite end of the spectrum: He *has* "plans".....oh so many "plans" that he actually has to MAKE UP needlessly convoluted plans to flaunt how intelligent he is. Riddler believes in games, believes in games with "rules" in a way the Joker philosophically cannot.
So in TDK, we've got a villain who wants to tear down Batman's dream of Order in Gotham because he wants Chaos.
For Batman 3, I think it would make sense to turn that around and have someone, The Riddler, who wants and believes in "Order" to a terrible extreme.....
....in a way, just as Gordon presaged the appearance of The Joker at the end of Batman Begins, I think The Joker predicted the rise of The Riddler in TDK:
when he says:
Do I really look like a guy with a plan? You know what I am? I'm a dog chasing cars. I wouldn't know what to do with one if I caught it. You know … I just do things. The mob has plans. The cops have plans. Gordon's got plans. You know … they're schemers. Schemers trying to control their little worlds. I'm not a schemer. I try to show the schemers how pathetic their attempts to control things really are....You know – you know what I noticed? Nobody panics when things go "according to plan"…even if the plan is horrifying. If tomorrow I told the press that, like, a gang-banger will get shot, or a truck load of soldiers will be blown up, nobody panics, because it's all part of the plan. But when I say that one little old mayor will die…well, then everyone loses their minds!
So I think it should be The Riddler because.....he's the complete opposite of The Joker; he's "a man with a Plan"
and this Batman 3 movie could be a real, real commentary on how scary it is that people are "willing to give up their freedom for their security" (for which they deserve neither...)
the whole point being, that if you think about it, Gotham has essentially put Batman in a position where he's a super-legal law enforcer; he's like a dictator in ancient Rome. Batman's rule is that he won't kill: this is what separates him from the chaotic villains like the Joker. But what separates Batman from basically being a tyrant? It's a very thin and blurry line: similar to how Lucius Fox was upset that Batman would use the sonar-tracking system, but in the end, Batman destroyed it because he only wanted to use it for the extreme danger that the Joker presented. But another man, i.e. the Riddler, might not have done that.
****So after the chaos that the Joker brought to the city, it would be disturbing but true that most of the people in Gotham would want someone to "restore Order" a "man with a Plan".....and even if the Plan is HORRIFYING, that people would still accept it, because its "Order".
So the way I see it, The Joker primed Gotham to be in a position where they'd ACCEPT the Riddler (knocking over mob bosses, establishing his own rule over the city possibly through high-tech surveillance that Batman is unwilling to use) if it means restoring Order, "even if the plan is horrifying"
so thematically, I think Riddler would actually make a lot of sense