Violence is like fire, it must be contained or it runs wild.
Violence is like fire. It does not exist everywhere and in every time and place. The answer to every situation is not a burst of Halon gas.
One thing that hasn't really been discussed (although Janet sort of alluded to it) is the distinction between risk and consequences. If the risk of an event is high, it calls for a response, even if the consequences are low. For example, if you've got an inconveniently placed coffee table in your living room, so that people bump into it frequently -- not enough to fall, but enough to get a bruise -- you probably want to do something about that. If the risk of an event is low, it may not call for a response, even if the consequences of the event would be quite severe. If you're confronted in your house by a polar bear, chances are you'll die, but I don't have a polar-bear-proofed house. Those people who live in that town in Canada that's on the polar bear migration route...well, they might want to make some different choices, including, y'know, moving five miles down the road or something.
The term "violence" is too generic to meaningfully assess risks and consequences. The risk of the sort of stranger attacks that make up the ludicrously stereotypical "scenarios" in the typical "self-defense" mentality: low. Consequences, if such a thing ever did happen: high. Opportunity to avoid such situations: also high. What does it add up to for you?