As someone coming from probably the farthest you can be away from it, I have a few thoughts, many match those above - other than proximity.
However the proximity issue does mean I've walked my local track already (600mile) so if it applies it is probably the primary one for most.
It is an institution. Long Trail claims aside it is considered by most around the world as the oldest
long distance hiking trail around.
Many other trails claim inspiration for their existence on the AT my local included.
It has a "community" - both the annual transient population of hikers and the angels, towns, and associated businesses and people along the way make up a hiking related community not matched anywhere else.
Despite it's proximity to "civilisation" it tries very hard to remain a "wilderness" walk.
Yes Bryson "was a candyass" but he made it even more well known.
Nearly every other trail has a much lower % of "newbies". Personally I think they provide much of the character and pleasure of a trail. Only hiking with experienced hikers is so much less entertaining.
Whilst "trail magic" exists on all trails, only on the AT is it so institutionalised.
And lastly for me, tell me where else I can go and spend six months in a foreign country that speaks english (sort of
), has good cheap food readily available to buy, only occasionally shoots a visitor, has few rampaging diseases and all for about $5k?