Does it have to be a fight to the death? No, that's your choice. You want their stuff than kill them, but if you want to be merciful than let them live. That adds the freedom of choice. Of course you get money regardless of killing them.
This makes me think, with the new finishing move system, it would be intereseting to see an execution option.
When the enemy gets down to maybe 10% health, they drop to their knees or whatever and you get to choose whether or not to spare them or execute them.
And the choice you make could change your reputation to either a brutal gladiator fighting only for the joy of killing, or a merciful gladiator, fighting only to make a living.