Makes sense. I think Nolan later changed Gotham to Philly, but even now folks think of it as Chicago. When I lived in Chicago, Google Maps listed my office building as the "Gotham City Courthouse," because that's where the exteriors were shot, lol. I still see Gotham as an East Coast city for the reasons you mentioned.
Back when Wizard Magazine put out their version of the "Ultimate Justice" League idea, they located Metropolis and Gotham close to one another, and they put both GL and Flash in California. I think it was a way to explain the frequency of those team ups.