My statement was not meant to be taken so literally.
That's just it, though -- Gotham didn't become a "gothic, crime-ridden hell-hole" until Frank Miller and Tim Burton came along. For the majority of its history, it was just a city like any other. (In fact, it was actually called New York in one of the very early issues.) It had as much crime and corruption as would be typical for any vigilante-based adventure story, but it wasn't portrayed as fundamentally any more corrupt or awful than any other city in DC Comics. (Heck, people say Metropolis is the bright and happy one, but in the early Superman comics and radio series, it was a hotbed of political corruption and racketeering.) And in the Silver Age, when comics lightened up under the Comics Code, Gotham City was no less appealing a place to live than Metropolis or Star City or Central City or any of the others. The darkening of Gotham began with The Dark Knight Returns, which posited a dystopian future where things had become utterly horrible, far worse than in the present. Then Miller did Batman: Year One and established the idea that Gotham needed a vigilante in the first place because the law was too corrupt to do its job -- but the implicit idea was that it was only that bad in the past because there was no Batman or Commissioner Gordon yet. However, later Batman writers neglected the "period" settings of both and portrayed present-day Gotham as a mix of both, a dystopian hellpit so corrupt and decayed that you wondered why anyone even lived there. And it got pretty ludicrous how far they took it.
So I don't feel that Batman stories need a Gotham that's constantly, incurably corrupt. As an incentive for Batman to have started in the past, okay, that makes sense, but if it just stays so awful despite all Batman's efforts, then doesn't that make him a failure?
Also, when did it stop being Gotham City and just become Gotham? Nobody ever seems to use the full name anymore.
Superman's been active for over a dozen years. I'd be surprised if Kara Danvers and James Olsen were the only two people inspired to follow his example. So yeah, there could be other crimefighters we haven't met yet. The longer the series goes on, the more likely it is that we'll meet some of them.
Personally I hope it's the modern, gritty Gotham City. Just because it makes that line so much funnier. And it's not like we're going be spending a lot of time there in a show about Supergirl anyway.