Sure, you don't personally need guns, but you do need physical safety at each end of the communication. Physical safety is provided by people with guns.
Police response times will never be low enough to be physically preventative outside of special areas (airports, stadiums, high traffic areas). It doesn't take that long to mug somebody.
Police violence is more of a way to discourage wrongdoing on the part of rational actors. Irrational actors (terrorists, mentally ill, drug-addled, enraged, desperate) probably won't be affected short of an oppressive police state.
Police has no requirement to protect. Also, there are people who live in areas where the police response time is 1+ hours even for the most drastic issues.
