I never said I didn't "like" the ship being named Enterprise, simply exploring a realistic reason for a models absence from a wall.
Which universe is the alternate one again?
In Storm Front, part two, Daniels said this: The timeline's resetting itself .... all of the damage he caused, it never happened
From that I get that basically the first two seasons of ST: Enterprise existed in an alternate universe. What the NX-01 did originally in the prime universe is difficult to say. But whatever it was, it would have been at least somewhat different than the events depicted on the show.
The first two season are not a part of the history of the other series, any more than the events of In A Mirror Darkly.