In Deep Space 9, once the war began, the same officers were assigned to the Defiant as were running Deep Space 9. Keeping this in-universe, wouldn't the skill set of officers who run a space station be different than the ones who run a starship, especially at war?
Because the ship was assigned to Sisko/DS9 and wasn't autonomous in the same way other starships were.
Even though the Defiant was designed to be a warship, the project was abandoned and the unfinished prototype had never been put in use. Sisko requests it with the sole purpose of deterring a Dominion attack by showing them that DS9 can defend itself if necessary. The Defiant was a flashy ship with a lot of teeth so Sisko thought he could show they were prepared to defend DS9 if they had to.
SISKO: You'll have complete access to the ship evaluation reports but to put it simply, it's overgunned and overpowered for a ship its size. During battle drills, it nearly tore itself apart when the engines were tested at full capacity.
KIRA: And this is the ship that Starfleet sends us to fight off an attack by the Dominion?
SISKO: We're not going to fight the Dominion, Major. At least, not yet anyway. Our mission is to take the Defiant into the Gamma Quadrant and try to find the leaders of the Dominion, the Founders. We have to convince them that the Federation does not represent a threat to them.
BASHIR: What if they don't believe us?
SISKO: That's why I asked for the Defiant. She may have flaws, but she has teeth, and I want the Dominion to know that we can and will defend ourselves if necessary.
Given DS9's strategic value to the Dominion, the Federation (and showrunners, of course) felt that it was ridiculous to expect DS9 to be able to defend itself using only runabouts.
At one point, Robert Wolfe and I were sitting around after the 'Jem'Hadar' episode had been filmed. We were looking at dailies and said, 'Jesus, we're blowing up Galaxy Class starships; these guys are tough, and all we have are these freaking runabouts' [....] We had to come up with a ship to combat [the Dominion]."
The Defiant was intended to complement DS9's fleet of runabouts, giving them a faster, stronger ship to perform away missions and protect DS9 from the Dominion. The show's producers even referred to it as "a beefy runabout." (Star Trek: Deep Space Nine Companion, p. 162)
As such, it made sense to be piloted and operated as an extension of the space station in the same way normal runabouts were.
In universe, the Defiant was a prototype, and consequently rather valuable; the Federation would likely prefer that it be crewed and commanded by only the most trusted personnel.
Defiant was "attached" to DS9 for station defense, and had little in the way of on-board living accommodations, so it makes sense that personnel would come from the station. As the commanding officer of the station as well as one of the ship's designers, it's not a huge leap to imagine Sisko would want to captain her himself.
From S3E9, "Defiant":
SISKO: Then bring me with you. I can help you stop the Defiant and prove our good faith. I was in charge of the shipyard where the Defiant was built... I helped design it. I know her vulnerabilities... her weaknesses...
The Defiant would likely make regular patrols of the area but we only see the occasions when Sisko and friends are running the ship; it's not clear if there are other patrols run by other crew members.
Out of universe: It's where the action is, so that's where some of the main characters are going to be.