I assume that any criminal who would kick down your back door and come into your home while you are inside, is ready to kill you, rape your wife and, steal your property.
That man should be ready to die when he enters and should get his wish.
The best security system in this instance, is a firearm in the hands of someone who knows how to use it
I agree with most of your post. An alarm will wake you up or alert you that someone has entered.
More importantly the existence of an alarm tends to deter most criminals.
At 4:45 PM, too. Perps clearly were intent on evil.