It will also depend on how many Naval Command facilities you build. If the range of those facilities is large enough then you don't need to put as much command infrastructure on the ships.
As far as I understand there is now a difference between Admin Commanders and Fleet Commanders. You only carry Fleet Commanders in flag bridges and Admin Commanders in naval head quarters.
The Flag Officers are the leader of any fleet they are in and the most senior flag officer is the fleet leader and give a reaction bonus to the whole fleet. When you detach a sub-fleet it essentially becomes a fleet and if it has a flag officer that might be junior to the fleet it was part of will now be the leader of that new fleet.
In my opinion the name Fleet is perhaps not the best because fleets are not really fleets but Task-Groups or multiple Task-Groups in one location, but that is beside the point. Admin Commands are more like fleets or even higher command structures. In real life fleet or theatre commanders rarely go with the ships they command, their position require them more of a top down perspective.