When did the E-D begin to be called the flagship? Thinking of it, it does not make sense. The Enterprise often goes to missons absolutely far away from Earth, to small pre-warp planets (those always seem to invite a Prime Directive breech, btw), or trivial assignmests like ferrying cargo (as important as scientific experiments and medicine relief, but still, hauling cargo). Missions any other of the hundreds or thousands of smaller vessels could carry. A flagship should be carrying diplomatic missions and signing military treaties, and most importantly, be always between SF Command and main planets (Earth, Vulcan, Andoria, The pigfaces I forget the name....). And have one or more Admirals on board. Flagship = Flag officer, no? The Captain only is there to take him from one place to another. Nothing of that happens on Picard's vessel.