In Sisko's absence, somewhere early in Season 5, I think, Kira and Worf have a disagreement, and Worf states that while she commands the station, he commands the Defiant.
Worf also moved his quarters to the Defiant, so I think we can assume that Worf in effect filled this role, though it was never established formally.
As to why Starfleet would commission a ship without its own bridge crew, it's established when the Defiant is first introduced that this was an experimental design that Sisko had helped develop originally to combat the Borg. Officially an escort ship, unofficially a warship. Kinks in the design had never been ironed out, however, and the ship had never been used, until Sisko is allowed to dust it off by special request for the crew's trip into the Gamma Quadrant to contact the Founders at the beginning of season three.
In other words, I would say the Defiant was not a standard Starfleet vessel, but a special case related to Sisko's command and the sudden strategical importance of DS9.
From a storytelling point of view, the show didn't need more characters, but it needed something more impressive than a runabout for the crew to get around in.