Good thread topic.
I'm going to ignore the fact that Batman and his villains are symbolic. For them to have any memorable value in the story they need outfits or a unique personality. Lets just pretend the comicbooks are a real world. Its a bit dumb to over-analyse these things and apply real world logic to these characters (like I'm about to do), especially since their entire existence is to be entertaining, but what the hell, its fun.
Okay, we could argue they're responding to the concept of masked identities when they see a caped crusader in their city. Seeing some dude dressed up as a Bat and having various Bat-themed gimmicks in his arsenal and Bat-puns in his vocabulary would inspire any crook with a mind for theatrics to take on their own gimmicked personality, especially if it makes you feel empowered, boosts your confidence, or feeds your ego (just how many of these villains were meek losers before they took on their criminal exploits? Exactly. Even Bruce Wayne is just a spoilt wealthy child who enjoys wallowing in his grief and wants to convincing himself that his predicament is unique (especially since not having to work gives him a lot of time to mope around the mansion). Masks do give you a sense of empowerment. Batman is in the same boat as his villains and he's in a cycle he will never escape, just as they are.
Jervis Tech may enjoy Alice and Wonderland and have various mind-control equipment, but the extra theatrical step to join them together seems to respond to the presense of the costumed hyper-theatrical Batman. He provides a precedent for it, but the crimes were likely to happen anyway (he might have just ended up date-raping Alice without the gimmicks).
Does that make Batman responsible? Not really, he just inspires the criminals with a useful symbol to channel their natural drives, the same as if they were inspired by Al Capone or anything else really. In the same way that the individual bat Bruce saw one night outside his mansion window is hardly what transformed him into a vigilante, even if it inspired his particular gimmick.
It may depend on how much the concept of masked villainy/heroism is inherent in superhero comic societies. There seem to be plenty of hints which suggest that Batman etc are just the recent examples in a long history of masked superheroism/villainy. In the Hush storyarc I remember there being sequences with a young Bruce watching heroes fight it up in the skies above Gotham, and even BTAS had the Grey Ghost (voiced by Adam West no less), and was a direct inspiration for Bruce to go the costumed route. If egotistical superheroes and supervillains are a fundamental part of these societies, then the individual Batman can hardly be blamed (he'd be just as much of a victim as the villains would claim to be).
Either way, their birth names should give it away. Joe Kerr (if you agree with that name), Victor Frieze, Maxie Zeus, they seem like they were all conditioned at a very young age to take on their particular gimmicked crimes. It'd be something so finely mixed into who they are since they were children. Its fate. Otherwise Joe Kerr would have become a humorless botanist enamored with plants and calling himself "The Foliage Freak", or Dr Freeze would fall into a inconviently placed vat of fire and only survive by walking around in a suit filled with fire and firing fire from a firegun. Batman may just have been a gentle push down the hill they were already hurtling down (ignoring the fact that these names are tailor-made for their powers... remember, I'm pretending they're real people).
I'll definately say that I think Batman helps to feed that psychosis, but he's just a very willing audience. The Riddler would still be leaving Riddles for whoever will listen, Joker would announce his crimes, Two-face would only knock-off places with two/double/twin/pair/gemini/couple in the title. All of their crimes are for attention not for personal gain, and deep down they want to be caught and helped (subconsciously. anybody who is serious about not getting caught would never leave a clue or announce their crime). If its not Batman, they'd focus their attentions on Commissioner Gordon or their parents or the mailman or anybody else who seems worthy to the challenge. That, or they'd manufacture their own hero (which is in part what they're doing when they torture the hell out of innocent victims, they're attempting to create their own nemesis).
Taking Batman out of the equation might send them into a melancholy for a while, but these villains are natural performers, and they'd find an audience soon enough, even if they have to lose the outfits and gimmicks.
No, Batman did not create these villains. His image may have inspired them, but under the circumstances they were all likely to commit the same or similar crimes due to deeply ingrained inability to empathise, accompanied by deep-set insecurities which mean they require people pay attention to them and recogise their greatness and talents (often wrongly imagined) by force.
