It doesn't belong in the Air & Space Museum. It belongs in a museum that specializes in artifacts of its type. Honestly at Air & Space it feels diminished by what's around it. Hard to take a fictional spaceship seriously as an artifact when it's neighbored by craft that actually went into space.
I agree with this. Any contribution made to the space program by the Enterprise
model was in the area of public relations. It just doesn't measure up to actual air- and spacecraft that achieved real-world accomplishments (often risking real lives in the process) that count for much more than just entertainment or even inspirational value.
If I'm not mistaken, the Smithsonian has a museum devoted to TV and motion picture arts. That's where it belongs.