I guess it depends on that old argument: Is Starfleet a military organization or not?Eh. I would hope that the "flagship" would have the best of the best.
See, in strict navy parlance, a "flagship" is the ship in a battle group where the overall battle group commander is based. But the Enterprise isn't a battle group flagship; it's the "Federation flagship." But clearly neither the leaders of the Federation nor the top commanders of Starfleet are based aboard her.
Maybe the "Federation flagship" is just a fancy showboat for ferrying dignataries around and attending diplomatic ceremonies (they certainly did a lot of that kind of thing). Wouldn't necessarily want to waste your best crew on a glorified taxi.
OTOH, the civilian use of the term "flagship" usually does mean "the best of the best" (although almost always referring to something other than actual ships). But I just have to wonder (at least, based sole on this episode) how "the best of the best" ever ended up with such a piss-poor first officer.
