Probably because all you really need is one APC, their job is to explode somebody and deliver bursts of damage that people haven't got the gold to defend completely against without sacrificing their own ability to team fight.
Also their damage isn't consistent since they don't Autoattack for damage so if they do their combo and the target lives, the target can continue hitting and possibly eliminate them before their CD's go down again whilst healing up :'P
tl;dr you don't need a lot of AP, just some.