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. <PERSON> 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 <PERSON> thought he could show they were prepared to defend DS9 if they had to.
<PERSON>: 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.
<PERSON>: And this is the ship that Starfleet sends us to fight off an attack by the Dominion?
<PERSON>: 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. 126
We have to convince them that the Federation does not represent a threat to them.
<PERSON>: What if they don't believe us?
<PERSON>: 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.
DS9: The Search Part I
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, <PERSON> and I were sitting around after the '<PERSON>' episode had been filmed. We were looking at dailies and said, '<PERSON>, 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]."
Captains' Logs Supplemental - The Unauthorized Guide to the New Trek Voyages, p. 79
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. 126