In the original timeline the NX-01 was destroyed months into its mission, and probably deemed as a major failure by Starfleet, hence its lack of mention. And the XCV-330 being the far more prominent vessel named Enterprise by the time of TMP.
However, its survival for the decade likely altered that. And the NX-01 is actually remembered by the time of STID. Meaning the TCW actually altered the timeline. Even though the timeline was supposed to have repaired itself when Vosk was defeated, meaning the NX-01 should have been destroyed and forgotten about. Of course, Starfleet may have just given Archer another NX-vessel to captain to deal with the Xindi threat.
It does also suggest that the events of "Regeneration" were supposed to happen anyways, meaning the Borg never actually altered the timeline in FC. The NX-01 was just never supposed to encounter the Borg, which they ended up doing, thanks to the TCW.