It's actually simple:
They get trapped:
1 haul job to your animal stockpile from where they were trapped.
1 reload cage trap job.
X haul jobs from your animal stockpile to your gear stockpiles for their loot.
They get killed outside:
1 haul job for their corpse.
X haul jobs from all the way outside to your gear stockpiles inside for their loot.
Basically, the 1 haul job of the cage shaves potentially hundreds of tiles off of the haul jobs for their gear, if you position your stockpiles carefully.
But then we have dozens of cages to make, and dozens of traps to reload, and we STILL need to actually get the Orcs killed off, which will require moving the cages AGAIN and attaching mechanisms to then, plus we'll have to clean up the bodies after they've been disposed off. Not to mention any cage trap triggered will be off-line until it's reloaded, unlike my current weapon traps.
In short, a whole STACK of extra jobs, at least one of which (attaching the mechanisms) can be done only by a few skilled Faerie. I don't have time between sieges for this sort of bulldikery.
I really get the idea you're confusing orcs and goblins.
orcs:
1, come in much greater numbers than goblins, especially early in the game. The number of cage traps required to seriously dent them would be prodigious.
2, Don't wear clothing worth recovering. I recover shields, weapons, arrows, and when there's traders around I order some armour items dragged to the depot, but a lot of the stuff I just leave to rot.