Actually, the main thing behind disarming a trap, is not getting hit/affected by it.
I assume you're talking about the rigged-shotgun traps, as you could never pick up bear-traps in the first place, and you DO get regular/concealed mines, AND you get the grenades if you disarm a grenade-bouquet.
One reward for a successful disarm of the shotgun, is the xp. Not a lot, but something. Of course add in well-rested, and two (or was it three) levels of the xp-boost perk, and it's not bad.
The other reward, is you DO get the ammo, if nothing else.
Every time I've looked a bit closer at the rigged-shotgun traps, most of they time they don't even look like full shotguns, more a modded tube. But I can understand wanting the actual gun to repair something else with, or just sell for the few paltry caps. Considering the type likely used, there's really not much you'd get for it