To Brave the Storm
Is there actually a reason for the NX-01 to be in mothballs? Considering Starfleet's losses during the Romulan War and that it still seems to be a functional ship, albeit battle damaged.
NCC-1701 is suppose to be the first Federation ship to have the name Enterprise
indicated that the ship was too badly damaged in the Battle of Cheron to be repairable. As for why they couldn't rebuild it... well, maybe there are reasons for that. All we know is that, as BillJ
said, there is no Federation ship named Enterprise
Is that really true, though? Maybe there could have been another Enterprise
in the years between 2161 and 2245, just with a different registry number. Unless, of course, it's been actually stated on-screen somewhere that the NCC-1701 was absolutely the first Enterprise
in Starfleet and I just don't know about it, which is certainly possible.