With prior arrangement, it is possible for two people, going to different destinations to meet up in the departure lounge and swap passports so as to allow a miscreant to go to a destination to which they are not entitled.
I understand it's to catch those who have swapped passports on the plane and left the old one on board.
Neither of these makes any sense as an explanation. As DaveReidUK pointed out, how would a passport check at aircraft exit discover anything different from the standard passport control at immigration? Either the pax shows up with a valid passport, or doesn't. Where and when the pax obtained said passport prior to arrival makes no difference.
Also, those who may be hoping to pick up new papers from a 'delivery person' before their reach the main control area.
The aircraft exit check would catch this, I guess, but who would do it, and why? Why not just have the passport sent to you in advance? And I'm not sure there'd be anything inherently illegal in collecting new papers on arrival - as long as the papers themselves are legitimate. If they are forgeries, or genuine docs in a false name, then they should (ha!) be detected at the standard passport control.
it prevents the person going 'awol' between the plane and passport control
This, and checking international transit pax, are the only plausible reasons mentioned so far.