For the exact reason throughout your post, because it looks cool or unusual to people, thus forming a strong appeal to the designs.
Yeah but way too often it just ends up reeking of desperation to make up for
game shortcomings they can see a mile away but are too lazy to actually address directly, especially for
a third-person shooter.
Grand Theft Auto (and Saints Row to a lesser degree) has the appropriate balance for a sandbox game - yeah they have helicopters but they're not the main focus, which should be foot action. Just Cause and Mercenaries try to do too many things at once.
Well with AC:AH, there is the ASF-X Shinden II operated under the USAF and Japan Air Self Defense Force, but that is strictly a downloadable content piece and isn't packaged into the main game as a special unlockable or as an enemy ace like in most of the older games in the series.
AC isn't quite as bad as people make them out to be, plus the ASF-X was designed by the same guy who gave us Macross - and he actually has an aerospace engineering background.