Often time the name Enterprise is given to the first or second vessel of a line, or a vessel involved in exploration. As such they are often the most advanced vessel in a fleet technologically or design wise. Even the word Enterprise has connotations of difficult undertakings, taking on new ventures, initiative, leading the way.
Also Flagship does not only refer to the best or most important ship in a fleet, but the ship that carries the commander of a fleet or subdivision of a fleet. As such the Defiant served as the flagship of the second fleet on occasion. In the movie First Contact, the Entrprise-E is not the flagship, but the unnamed vessel of Admiral Hayes. Once it is destroyed Picard takes command of the fleet.
Also, as far as I can find searching the transcripts the only time the Enterprise is referred to as a "flagship" in The original series era is the reboot. The word flagship is mentioned in TOS in the Balance of Terror and Enterprise Incident referencing Romulan Flagships, and the Corbomite Maneuver in reference to the Fesarius. (If I have missed something from the TOS era comment on it and I will remove this section)
Here are some historical examples culled from wikipedia:
- HMS Enterprise 1774 - first of a class of 6th-rate frigates commisioned by the British Navy
- USS Enterprise 1775 - first sloop-of-war captured by Colonial Navy
and acted as flagship of the Lake Champlain squadron.
- Enterprise 1814 - first steamboat to successfully navigate the Ohio river from Louisville to Pittsburgh opening up a new trade route.
- HMS Enterprise 1848 - Arctic discovery ship making boyages to teh arctic from both the Pacific and the Atlantic.
- Enterprise(ballon) 1858 - second of 7 balloons built for the US of use in the
civil war. Used in demonstration that led to the purchase of the
- Enterprise 1862 - first in a lone of sternwheelers that would traves the Fraiser River in British Columbia
- HMS Enterprise D52 1918 - One of 2 Emerald class light cruisers with prototype twin 6" turrets. Lead ship in Assault Force "U" durring invasion of Normandy.
- USS Enterprise CV-6 1938 - US aircraft carrier regularly used as
flagship for squadors of other ships durring WW2, equipped with
- USS Enterprise CVN-65 1958 - First nuclear powered US aircraft carrier
- HMS Enterprise A71 1959 - Echo class survey ship
- Space Shuttle Enterprise 1972 - Prototype orbiter
- HMS Enterprise H88 2002 - Multi role survey vessel of the Royal navy.
- VSS Enterprise 2009 - First Virgin Galactic commercial