It actually goes beyond brains or lack thereof. When I did the cap pistol exercise with a friend, we figured out that all told, the cc holder has about 3 seconds total of non-contiguous advantage over a robber who is brandishing.
That is a ridiculous advantage in a gunfight.
The robber doesn’t want to shoot you, he wants to rob you and leave. He expects you to dig around in your pockets. He doesn’t know you are armed. It takes time for it to register with him that your gun is not a wallet or something, and that is only if he is facing you when you draw down on him.
And one of those things cops don’t mention very often is that about half the guns used by criminals are non-functional. Though you can’t count on that, it is still nice to know.
Finally, overlaid over all of that is that the robber has a brain the size of an oyster.