If they expect people to be armed, it's much simpler to just kill them before they can mount a reaction. From the point of view of a criminal who already committed crimes sufficient for life imprisonment, that's a very easy choice.
If criminals expect people to be armed - they'll move on to easier targets.
That’s objectively wrong and goes against every single study on the subject.
The best overall strategy for survival is to be cooperative and not surprise the attacker. Armed victims have a lower chance of survival because, again, they are not expecting the attack. If the victim starts a reaction, they usually get shot.
When every single citizen CAN be carrying a gun - the criminal WILL think twice before engaging in stupidity. If not the victim, then the random bystander or nearby family member can make a colander out of criminal engaging in active crime.
When possibility of this is present and political and legal system is supportive to keep our streets clean - the crime will cease or be reduced to minimal levels.