Waiting till the last moment also allows for the Klingons to veer off in case they were just doing their standard posturing.
And specifying targets is the one unrealistic
thing that Trek captains are typically guilty of. There's something like fifty of them there - but the station is perfectly capable of firing at as many. Sisko (or Picard, or Kirk) should say something less tactical and more strategic, such as "Inflict necessary casualties, but don't go overboard" or "Save ammo" or "Go all out, perhaps they will take the hint", after which the gunners would do their job. And Sisko sort of says the second thing, by specifying that only every second launcher be used at first.