The quick 'n' easy answer to that is "That never crossed Roddenberry's mind." He may or may not have created a back-story in which Vulcan and Earth help start the UFP and Starfleet; more likely he imagined it all beginning with Earth. Indeed, the Vulcan ships weren't even really planned out unless a script really required it, so the few designs we see differ wildly. We never see the T'Kumbra in the DS-9 episode "Take Me Out to the Holosuite", and the ship that lands at the end of "First Contact" looks nothing like the starships that came to be regulars on Enterprise.
It seems, however, that the Star Trek universe allows for a bit of leeway here. Although we never saw a Vulcan spaceship until Star Trek: The Motion Picture (a small shuttlecraft), there's nothing to indicate that Vulcans don't have their own starships, or can't fully populate a Constitution-class vessel. Maybe the Intrepid was given to Vulcan as part of an exchange program. Although Gene Roddenberry had high hopes for mankind's future, it seems that prejudice still rears its ugly head on Star Trek, and the Vulcans are no exception. Many of them do not care to be around humans in person, preferring to help them from a discreet distance. Maybe a crew of Vulcans running a Constitution-class ship was a good way to facilitate things.