To be sure, the ENT Intrepid
was basically just as large as NX-01. Archer's ship isn't marketed as Earth's first starship at any point of the show: it is only marketed as the first of Earth's supposedly many starships that is capable of warp 5 travel and subsequently exploration of areas that remain unknown to Earth.
One might assume that Earth's Starfleet (or UESF for short) had a lot of relatively weak but still reasonably large warships for show. Since UE couldn't do any meaningful exploration with the old engines, but still had the technology and resources to build ships such as the Boomer transports, construction of a showpiece warfleet would seem like a natural step for the government to take.
Once other navies joined in and created the UFP Starfleet, it might be that Earth's dedicated exploration ships remained the combined fleet's only dedicated exploration asset. The older players might have already explored all they wanted, and would no longer have dedicated ships in their inventories. Thus, when the UFP Starfleet began to profile itself as an exploration organization, Earth hardware would be a major influence.
Half a dozen other lines of speculation are equally valid, though. Neither ENT nor TOS requires us to know anything about the size of Starfleet off screen, and the episodes would play out much the same regardless of whether there were two other ships, or twenty thousand.