Non-lethal mode is primarily made to give the player an option to avoid killing temporarily hostile NPCs, such as civilians, quest givers or vendors who catch you in the middle of a criminal act. Without it the player would be forced to kill them which would be just terrible design.
Outside of that in terms of the story as much as I wish it did, for example with Minthara's story, it unfortunately does not have much purpose. Still it's incredibly useful as you can also use it to grab unique items off of NPCs without having to kill them, such as Kagha whose unique necklace can be obtained by knocking her out
