Wild Bill Hickok frequently carried a pair of matched revolvers. But there’s no evidence he ever used his left hand in a gunfight—he rarely even practiced shooting with that hand (and when he did, he didn’t hit what he was shooting at).
Instead, the shootist used the second gun as a backup. If he ran out of bullets with his primary weapon, he could pull the pistol on the left side and fire—with his right hand.
Or he might use that second revolver if the powder got wet in the first gun.