I don't see why the Arkham name couldn't be fit to a Silver Age-ish prequel story. Over-saturation can be a problem. All you have to do is look at the yearly Assassin's Creed and Call of Duty releases. But I'm not sure that's the case here. There were two years between Asylum and City and if the newest game comes out late this year, that will put two years between City and the new one. My guess is still that they have a new team cranking out a sequel to get on the tail end of this console cycle, while Rocksteady works on something more ambitious for the next generation. This could be a smart strategy just so long as they put a quality team behind the title, and given the success of the franchise, WB would be crazy to not invest in a solid developer.
As far as vehicles, I think the bat-cycle would be a better fit than the batmobile. The reason the gliding/grappling mechanic was so satisfying is that it was a seamless transition with the rest of the gameplay. Everything moved smoothly and you could fluidly combo from navigation to brawling and back. I think the cycle would be a better fit for that, more maneuverable and easy to hop on and off of, nimble too. You could call it with a button, hop on from a nearby building or glide onto it, cover some distance, grapple right off, or fling yourself off of it and into the spine of a thug. I would like to see bad guys using cars though. I want to drop onto the roof of a getaway car and pummel the driver through the windshield.
I'd like to see smarter bad guys that communicate better and require more flexible planning. Part in parcel with this, I'd like to see more focus on stopping crimes that are actually being committed. In the core "dungeons" of City, everything felt a bit detached, traveling from one puzzle room to the next without any communication between the guards. I'd like to see more seamlessly communicating thugs. I'm picturing, say, a bank robbery, where you have thugs with hostages in the lobby, a spotter outside, a getaway driver, and men in the vault, and the way to approach it is open ended. Do you go in for the hostages first? If you hit someone else and aren't stealthy enough to take them out silently, the hostages will get shot. Or do you start with the driver, cutting off their escape. Or sneak in through the roof and silently take out the guys in the vault, to lure the guys in the lobby from their hostages and have better access to take them out.
I'd like to see part but not necessarily all of the environment to forego the "a bunch of thugs trapped in a space together". Whether that's instanced spaces or parts of the city around a quarantine perimeter populated with cops and civilians, an element of having to navigate around folks you aren't allowed to harm.
From a story perspective, I really want to see the exploration of what an Arkham without Joker is like. I could come up with a fantastic pitch (one that doesn't treat Harley like a stupid tart) but for now we'll just leave it at a deeper exploration of the rest of the rogue's gallery, and how crime changes in the city without such an unpredictable and prolific force of nature as J around. And let's get a story that's a little deeper and a little longer this time. Heh. deeper and longer....
I'd make the Joker baby the big mcguffin though. A Harley, untethered by J, who has become a ruthless and clever criminal, absorbing much of her old beau's crime family as she tries to secure her son's legacy. All the other rogues gunning for her, worried about the Joker's legacy living on and wanting the notoriety of stopping it in its tracks. And B trying his best to find and protect her and her or her newborn/unborn child. A police force reluctantly obligated to target Batman as a threat after the news hits that he allegedly killed the Joker.
A Gotham Knights direction could be fun too. Bring out the Metroidvania elements by giving various characters distinct skill sets to navigate the setting and chapters that reflect the style of a comic book crossover.