You scare people when you display a sidearm. Why do you think the cops carry them; it is the power of life and death. When weapons are concealed this fear does not exist. You cannot interact with people, especially strangers, on a day to day basis displaying a sidearm without envy, suspicion, derision, ridicule, anger, and other emotions coming into play. Concealed weapons nullify this problem.
If you scare people the politicians will take advantage of this fear to further their own ends. Politicians dont care that you support RKBA, they only care about what will get them votes. If the fear is not there the Politicians cannot take advantage of it to get votes. Concealed weapons remove a big incentive for politicians to be anti-gun.