But since it actually is a naval vessel, that's rather confusing. And I still say it's too fannish to force the in-universe characters to revere a particular ship above all others just because it's the ship that we fans get to follow on TV.
First off, the Enterprise
is not a naval vessel. It is a Starfleet vessel. Regardless of some of the similarities, Starfleet is not the modern military. They could certainly use terms differently in the 24th century.
Second, the on-screen evidence (there's that word again!) suggests that it is not being used in the traditional naval sense but, in fact, is being used in the "civilian" sense. And the on-screen evidence also points to the Enterprise
being considered a legendary and super-prestigious ship.
Now, that wasn't the case throughout TOS, I'll grant you. But I believe we are to look to TOS as being the reason the Enterprise
became legendary. Throughout TNG, the ship is several times referred to as "the flagship of the Federation," even though it is clearly not in the naval sense. There are no flag officers on board. The ship is usually off on missions by itself. It is not leading groups of ships. No, clearly the meaning used is that is the most prestigious ship, a ship of special distinction, which stands as a symbol of the Federation.
I can't find any canon evidence that would suggest that when Picard calls the Enterprise
the flagship, that he is using it in the naval sense.
ADDENDUM: Also, the Enterprise
is not the only hero ship we follow. We follow the Defiant
too. And the Defiant
, in fact, gets to be the lead ship of entire battle fleets. Yet never once do we hear either of this ships referred to as "flagships."