It's neither a dumb nor semantic argument. It's really two sides of the same coin. You need both to survive the aftermath if you ever use a gun to defend yourself.
If you're going to carry a gun (or any deadly tool), you really do have to be mentally prepared to use it. If you're not, you'll hesitate and you'll be on the receiving side. If you are mentally prepared, you're less likely to hesitate.
The "shoot to stop" idea is also part of mental preparation. If the goal is to stop, you're more likely to stop shooting once the threat is no longer viable, even if still alive. The legal aspect of this is real. Saying, "I just wanted him dead," vs "I just wanted him to stop," makes a huge difference in any court.
Also, whether you agree with it or not, once the threat has been stopped, any further shots make you the assailant. This is why I advocate starting with a controlled pair and then assessing the situation while moving.
All any reasonable person wants is to not be attacked. Therefore, stopping said attack is the goal. If the attack is not life threatening, no need to have the gun out. If the attack is life threatening, placing rounds on target quickly is very important. Aim for the largest part of the attacker. Not because this is the "kill" zone, but because bigger targets are easier to hit and you don't have time to pick and choose.