Starfleet having a ship named Enterprise on the "navy list" would prevent them having another starship named Enterprise. Be it the NX-01 in reserve, or a courier ship that runs from Earth to Jupiter. However that would be another ship named Enterprise in Starfleet, but definitely not a "starship". The NX-01 could also have been left as "active" in the way USS Constitution is "active" today. But even in reserve she would be on the "Starfleet list" until removed (scrapped, sold, placed as a museum, but not sitting in mothballs waiting for possible use, at least not with the name "Enterprise").
An alternative being that the Earth Starfleet and the Federation Starfleet are not fully integrated in during this period of time. The remains of UESPA staying around until the end of the 23rd century. Another Earth ship Enterprise would not count towards being a Federation ship Enterprise, even if Earth is part of the Federation at that point, by the nature of the services.
Another alternate being President Archer, for some reason, keeping that name from being used by Starfleet (names are still selected by the Secretary of Starfleet (or closest equivalent to the Secretary of the Navy) under the direction of the President of the Federation).
A final alternate is that the name was used by other member worlds space forces and Starfleet decided to respect that and not have one of their own until the 2240s. Not sure why this would be, but there you go.