A beaker full of death wrote:
It wasn't the Flagship, but it was repeatedly stated that the Enterprise was a special vessel and there were only 12 like it in all of Starfleet.
You mean like a WWII aircraft carrier, which was in fact the basis for the role of Starships in the Starfleet? The adventures may have been Hornblower, but the fleet was right out of WWII carriers. Just look at the names of the ships.
The Enterprise is not a carrier. Carriers travel in carrier groups. They have combat air patrols. They are floating airports designed to project military power via the aircraft.
She is much more a Hornblower type-ship. Alone, dealing in war, diplomacy, trade, and exploration without assistance. Her shuttlecraft are much more like the small boats that would be launched from the likes of the H.M.S. Indefatigable.