And that is what most self-defense training (which includes remaining within the law) teaches as well.
It is indeed what is taught. Where is the logic in stopping if the person is still a threat to you or bystanders? This isnt TV. The legal standard for shooting is very high and presumes you only do so to stop a lethal threat, gross bodily harm, commission of a felony, etc. In that case, you dont stop just to 'give the other guy a fighting chance at life.' The presumption is that they are still the same lethal threat until they are immobile, unconscious, dead, or completely submissive.
Police are actually reprimanded if they 'shoot to wound' btw in many cases. Because again...if the threat was lethal to begin with, you risk your life and the public safety if your 'more difficult shot' misses.
That is why police and citizens are also taught to go for the largest possible target: center of mass, COM, the chest.
"More than 700,000 law enforcement officers currently working in the United States have been given this or similar instructions in the academy"