By the time there is a response the attack will already have happened, so surveillance will not prevent the attack. Crazy or mentally imbalanced individuls by definition do not care about legal consequences, they could attack you right in front of a cop, that's why they are crazy.
The idea that antisocial elements will be discouraged because of surveillance basically translates into a surveillance state as there is no way yet in the modern world to predict how, when and by who 'antisocial' behavior occurs.
So you are advocating monitoring everyone in all public places 24/7 the idea being anyone contemplating illegal action is aware of the surveillance and modifies their behavior.
Won't getting some body guards be a better option than attempting to inflict a surveillance state on everyone in your quest for absolute safety.
Reasonable people accept there is a cost and tradeoff for freedom and liberty. One can make a case for better policing but this option takes us straight to the bottom of the slippery slope.