If I produced a Batman game, the first thing I'd conceptualize is a new combat system. No more rhythm-focused arcade score combos.
I would steal the rearward punch/kick from Streets of Rage series, let the player perform it by tapping the punch button on the face of the controller and pushing the stick to the rear at the same time.
The player would need to face the enemy in order to block, with R1 perhaps, instead of being able to block from any direction. I'd probably have Batman just hold his arms up defensively, like a boxer, rather than animate all kinds of different counters that slow down the combat and make it look more... sticky.
No more zigzagging around the map with this lame homing attack; instead you hold a dash button (Circle/B) to quickly close in on enemies, like in a real action game. Tapping it makes you step quickly to the side. No dodge rolling. I hate dodge rolling.
I would steal the targeting system from Ocarina of Time, let the player move sideways and backwards and also circle around enemies by holding the L1 button. They can switch targets by shifting the right stick. But there would also be a light auto-targeting system that activates when you come very close to an enemy, nowhere near as generous as it is in something like Bayonetta; only enough that the character doesn't end up punching air instead of the opponent they are pointing towards.
Cross/A would be the jump button, naturally. You would only be able to jump over enemies if you've brought them to their knees, instead of weightlessly hopping over them like in the Arkham games. Pressing jump after jumping would allow you to glide.
The attack button would be Square/X (punch) and Triangle/Y (more kicks, but not just). Pressing them longer would allow you to perform power punches and kicks. There would be a few combos, XXX, XXY, XYYX, YXY, YYXX, that kind of stuff. Press X and Y together for a special attack that has a cool-down.
I would mix fixed camera angles (that can be panned somewhat with the right stick) and standard rotational cameras; let the player switch between them by clicking the stick down (R3), like in Metal Gear Solid 3. The rotational cam would show your entire character and a good amount of space around them, rather than being another over the shoulder game, as is the norm now.
The stealth and combat would blend right into each other, meaning that you can attack and then disappear into the shadows again, instead of the stealth and combat always being completely separate like it is in the Arkham games. You would always have a choice between stealth and action. The enemies would not communicate telepathically, meaning that just because you've alerted one guy the whole gang doesn't instantly know where you are. Shadows would play a major part for the first time since possibly Splinter Cell. I would remove all the gargoyles and give the player other types of vantage points that aren't so conspicuous and convenient. To take an enemy down stealthily, the player holds one of the attack buttons and releases, preforming a hard attack that knocks them out. It doesn't knock them out in combat because they brace themselves for it. No chokehold or anything like that.
The D-pad would let you select your different items, the right trigger would let you use the item and holding the right trigger would allow you to prepare or aim it until you're ready. So you could also cook smoke grenades and explosives. If you want to cancel, you press the left trigger. I don't know if I'd use the whole D-pad for those gadgets or just have the player scroll left and right with Right and Left. D-pads are kind of crappy compared to number rows when you want lots of different items. Perhaps the player would be able to select between four items and assign different ones by pressing Options/the touch pad and opening a dedicated menu. Batman would have fewer items, only ones you can see on his person, some perhaps hidden in his gloves and boots rather than only the utility belt. I would even limit his number of baterangs, but let him pick them up.
He would be able to pick up items with the left trigger: bottles, pipes, bricks, even take hold of enemies' guns and then hit them with them by pressing the attack button. To compensate for the limited items on your person, there would be plenty of things to interact with in the environment. Because being Batman is about being resourceful. Instead of static photorealism, the graphics would be simpler, to allow for more breakables. Some of those smaller items that can be thrown could be used as both weapons and stealthy distraction. You wouldn't be able to use your own gadgets until you let go of the environmental item again, reason being that the right trigger becomes the temporary item's throw or hit button while it is in your possession.
L3 would put Batman in a crouch position. The crouch would not make your footsteps quieter, but instead only allow you to cover behind low objects and access low spaces. It would be designed so as not to interfere with combat should the player press it by accident; Batman would stand up and perform the fight action all in one quick animation.
The Arkham games' stories are hurt by being drawn out and crammed so full of villains. What I would do is design four or five loosely connected episodes, in which the villains are divided more or less evenly. Because we've never had a great Batman game anyway, I would have no problem bringing favorites like Ivy, Two-Face, Penguin and Catwoman back, but I also want to see lesser known characters, like Ventriloquist and even just mobster bosses and corrupt politicians or policemen -- non-supervillains. No Harley Quinn. She's played out. The animated series and games overused her.
Other playable story characters would be Robin and Batgirl. I'd probably make Robin a 13-year-old kid, like in The New Batman Adventures, because there aren't many games where children are beating up adults and I want to see how that would work mechanically. It would provide a nice contrast against the stronger, bigger Batman and Batgirl. Nightwing would have some cameos. He's be more an outsider who doesn't get that involved. Campaigns would be as follows, with the player able to choose any of those characters:
Batman
Batman and Robin
Batgirl and Robin
Batman, Robin and Batgirl
Batman
There would be some unique events depending on whom you choose, since they wouldn't always be together.
I would drop the XP and upgrade system and simply give the player every counter, attack and evade from the start. Unlockable abilities become a nuisance or overpower you when you want to replay a game and wouldn't work so well in this type of episodic game anyway.
Probably wouldn't make it open world. It's too hard to make an open world as interesting as a well made linear game. It can have hubs and some good backtracking, but no big open city.
If there are detective parts, I don't want to get to the solutions in such linear, boring ways. This might be one of the hardest things to get right.
I want simpler character designs. Stop covering them in so much armor. It takes away from the theatricality of those characters and doesn't show off their forms so well. The creator of Aeon Flux said it pretty well, when explaining why he chose to cover his protagonist in so skimpy, tight attire. It allowed him to be more expressive with her movements. I think he compared it to a ballet dancer or figure skater; can't remember exactly. I'm not gonna pretend he didn't also want to sexualize her, but it's obvious that he was speaking the truth when you see the way she moves and stretches, especially in those first two seasons where she doesn't speak. He said that it's the same for superheroes. That they wear skintight clothes so that the artists can be more expressive with their anatomy. I don't want this ugly mix of photorealism and comic dimensions, like in the Arkham games. Characters should be muscular, but not so roided out and rectangular. I'd probably give the characters realistic proportions and dress them up in styles somewhat reminiscent of David Mazzucchelli and Neil Adams' art and at the same time something that looks new. I'd make their faces original rather than photo-scanned; or if photo-scanned, then with enough editing performed afterwards that they become faces only existing virtually.