Which of course is not to say that on balance mass surveillance of public spaces is a net benefit. But it does have some benefits, and it does the debate disservice to deny them.
Heard studies that proves the opposite. The kind of crimes that substantially deterred by the chance of getting caught are crimes which the perpetrator has had time to consider for a length of time. Violence of the moment is generally not deterred by the chance of getting caught, and is practically unaffected by surveillance of public spaces.
Or to mention a few practical examples, road rage isn't effected by surveillance. A person being enraged at a bar isn't effected by surveillance, through a fight outside the bar could. Premeditated murder is deterred by the punishment/likelihood of getting caught, but other forms of murder isn't. Based on the theory, I would also guess that sexual harassment is decreased while rape isn't.
Not sure if violent acts are entirely random, I have not enough expertise on that. Currently I assume most acts of violence are not entirely random; and if they are, they are a mental/medical/neurological illness. And it might be perfectly normal to be dispositioned to be like this, but it would still be a problem.
How about allowing citizens to carry their own protection?