That idea is neat, but I think it would feel out of place considering the setup. The ‘bait’ aspect of the Death Star and the Rebel’s attack plan both hinge on the Death Star being hidden and isolated from the rest of the galaxy and the Imperial fleet. If the Death Star were to be constructed around Coruscant (or moved there at some point in its construction), there would be no way to keep that a secret and so the Death Star would fail to be enticing as a target to the Rebels since they would expect a trap.