Frodo (and others): This is somewhat related to our creating of alternate films. Can the 1989's Batman thing be done again, giving new visuals to an existing hero?
That doesn't only mean gothic, but any style that makes the final product stick out from all other contemporary films of its time.
It hasn't got much to do with how the story is written, only with what we see onscreen: the designs, the sets, the mood, the look of streets and buildings.
Let's say we come up with another one of our alternate films. We pick the hero, then director and cast. It doesn't need to stop there.
Why not find a visual style that could work for the particular hero?
It can be art deco, but much more pointed out than in Superman. There's also greco roman, anglo saxon, baroque and victorian/steampunk. To name a few.
If you want something a bit more modern (but less inspiring), there's something called functionalism. And maybe you've heard about brutalism too?
A DC superhero in a city that's overly brutalist and not much more, could that work?
Perhaps it's best to mix an older style with present day?
No, it's not set in the past. As in Burtonverse, the chosen style works in unity with (and overlaps) our own time (now it's 2020s). There's still modern technology, but everything is designed different than in the real world.
Not realistic at all, but this is an alternate fantasy world.