I cannot help wondering if the lack of public and media awareness of the Sea Harrier (and other aspects of naval aviation, if not the RN in general) made it more vulnerable to cuts.
I wouldn't have thought so. Most of the British public think of the Sea Harrier whenever a Harrier is mentioned, most probably because of the media coverage of the Falklands Conflict. Up until fairly recently the GR5/7 was known to many as "the Air Force version of the Sea Harrier."
We can usually trust the media to talk about Army helicopters, RAF planes and Navy boats - they're not all experts!