Gotham is whatever it needs to be. Funny that in the past decade it has taken on qualities from both Detroit and Chicago. It's tough to say Gotham is only New Jersey when Blüdhaven is even more explicitly New Jersey in relation to Gotham. But that is without getting into the weird explanation that DC's Earth is some percentage larger, as to accommodate all the extra fictional cities.
But Miller Daredevil stories makes sense against Miller Batman stories, especially with the Foot/Hand/League of Assassins all operating in the same space. As well as how Nightwing is literally the same acrobatic, street level character against Daredevil.