If, for example, the mayor of one of the most polarizing cities in the United States is violently attacked, nobody is going to say, "Yeah, but we saved $5,000 in police overtime." Ross Mirkarimi is pushing legislation that would require officials to repay security costs for time spent campaigning or on other unofficial business. 

If you're going to ever pay for the mayor's, or any other politician's, security, you should pay for it the entire time that they're in office. The fact that a mayor or governor would need security is certainly troubling, though ...