I think, personally, aside from the story being unnecessary and poorly written thanks to the firing of the writer of the first two titles, the real issue with this game is its lack of direction. Allow me to explain what I mean.
In Asylum, you're in a very contained space, and you are forced to progress to each area in order to eventually make it to Joker and, hopefully, escape the Asylum. This means interacting, whether you want to or not, with characters like Ivy, Scarecrow, Croc, Bane and more, because it's quite literally necessary for you to do so in order to progress.
In City, while you're in a much larger area, certainly, you're still at the utter behest of the enemies who control their own areas within the city. For example, you might be trying to get to Joker again, but you're also dealing with Zsasz's phone calls, and in the middle of that, you'll be pulled into an utter mad sequence thanks to the Hatter deciding he wants to screw with you for 20 minutes. Then, when you finally escape that, guess what, here comes the Riddler with another person for you to rescue, and oh also Mr Freeze needs you to save his wife, who just happens to be captured by Penguin. You are never given downtime, because someone always wants a piece of you.
But in THIS title, you have nothing but time. Sure the plot gives you a sense of urgency at times, having to rescue so and so and whatever, but overall the side enemies are rarely seen or interacted with outside of your own accord. Now, YOU have to find THEM. For instance, I was given the task of meeting with Hatter to find out why he's locked himself in the police department. It's not required. It's just a thing you can choose to do. But being given the choice is the problem. I want to be FORCED to do this. If I am not, why would I go do it? This game removes all the ownership the enemies have over your time, and now, interacting with everything is merely an option, instead of a necessity.
The problem with this game isn't the Batmobile, as many have said. It's actually the core mechanics of how to story works, and the poor story at that.