The E-D was said to be the command ship for the sector that included Minos Korva, the likely location of imminent hostilities. Quite possibly the peacetime Starfleet believes more in organizing its forces by operating theaters (using whichever ships are in that theater at the time) than in grouping the ships in fixed formations.
Also, Starfleet might believe in placing certain admirals in command of specific sectors or combat theaters, and separate admirals in command of specific wartime fleets. Nechayev, Ross and Haden might be examples of the former: the first for the Maquis area of operations, the second for Bajoran space, the third for Romulan affairs (later to be superceded by Admiral Janeway). Shanti from "Redemption" and Sitak and Coburn from "Favor the Bold" would be examples of the latter, and addressed as Fleet Admirals regardless of rank.
To be a fleet flagship, the E-D would probably need to have an admiral of one type or the other aboard. To be a mere "command vessel" would not necessarily require that. And of course the ship would always be the Federation Flagship by honorific, regardless of whether she was acting as a flagship to some fleet or not.
Timo Saloniemi