Let's look at an example:
You are walking late at night through a park with your dog (you worked late, and in the winter it gets dark early). You are approached by a man waving a knife saying "Give me your wallet or I am going to cut you!". You pull out Dieter (what, am I the only one who named his piece?) and let the BG look through all four inches of the barrel. You hear a sound similar to "Eeep!" and the BG runs away. You feel good because you did not let yourself be a victim, your dog feels good because he found a "good spot", and you didn't have to hurt anybody. Maybe that guy will give up his evil ways and get an honest job.
On the way out of the park you hear tires scream as two police cruisers screech to a halt. Four police officers jump out of their vehicles with weapons drawn and start yelling. Being compliant, you put your hands in the air. Now off-leash, your dog heads toward one of the officrs, tongue lolling and tail wagging. The officer dispatches him with two shots to the head. You discover that a felony takedown hurts even worse than it appears on television.
While you are standing, cuffed, beside a police cruiser, you notice another cruiser roll slowly by. Inside you see the BG crying, looking at you, and you see him say "That's the guy." Now mister BG has no knife, and you are a criminal who tried to accost/mug/shoot this innocent fellow. You become a felon (no more shooting of any kind for YOU), spend three years in prison, and come home to an empty home (the wife "met someone" while you were away), no job (they don't hire felons), and no dog. Somehow the dog hurts the worst. Oh well, at least you are still alive. Defenseless against the next attack, but alive.
If you had bothered to call the cops (what do you mean you carry a handgun, a BUG, three spare magazines, but no cell phone?) they would know that there was a BG with a knife matching the description that you give, and when he tries to make his call they know right where to find him. Now you are a hero, your dog is alive, your wife still leaves you (if she would leave you while you were locked up unfairly then she was not a good partner anyway), you meet a supermodel at the dog park who loves the way your belly gently laps over your belt, and all is right with the world.
As important as draw speed is, so too is speed dial.