There are a couple topics that cover left handed animations already. I think that it would be awesome! It's also the only reason I would ever switch from a normal control scheme to a southpaw configuration. If it doesn't appear left handed, I feel like I'm not being amply rewarded for enduring the torture of relearning how to play first-person-shooters.
On a separate note, it would be intriguing to have a WEAPON that was specifically left handed. My idea was for an exotic sidearm that could be called... well... "Lefty". This sidearm would be held only in the left hand, although ADS and trigger buttons would not change at all.
I think a funny description would be a conversation between Banshee-44 and some nub-like Guardian:
"Hey, Banshee, this gun's magazine eject is on the wrong side. Banshee? Banshee!"
And a very OP unique exotic perk could be to dual wield it when the primary weapon is a hand cannon. Of course, this would have to be paired with some significant downsides such as reduced accuracy and a sizable ammo cut to both weapons while dual wielding. Dual wielding would only happen when a hand cannon is equipped in the Primary slot, and the player switches to their Special
Other topics about lefties: