Someone in who can afford to live in a wealthy neighborhood in Chicago and who is concerned about being a victim of violent street crime in their neighborhood might reasonably prefer to pay a neighborhood association for additional private security, rather than engage in a city-wide political process and agitate for raising their taxes and using the proceeds to pay for additional police. Paying for neighborhood-level private security solves an immediate local problem, and in a place like Chicago there are a lot of political forces who do not want to see additional policing done and would want to use additional local taxes raised to pay for things unrelated to or perhaps even counterproductive to the goal of decreasing local crime by increasing policing.
>rather than engage in a city-wide political process and agitate for raising their taxes and using the proceeds to pay for additional police.
The thing is that they are more likely than non-wealthy citizens to be agitating city hall anyway. They'd just rather decrease taxes and have more control of their money than do anything to improve the city as a whole. If it gets too bad they just leave the city.