Would it make sense to have a "City" identifier?
Potentially, but that wouldn't be consistent with the current game and in my opinion isn't super necessary. "City" is, as quoted, a new card type similar to Covenants and Curses. This means that any card that is a combination of a Site and a Fortress is a City. Identifiers are generally reserved for things that describe what the card represents, not the card itself. The exception to this, of course, when the print on the card somewhat ambiguous, such as the territory class icon only applying to one side of the card.