Why don’t the routes run across fields instead of above residential areas?

Schiphol lies in the middle of towns and villages. It is not possible to draw a straight line from Schiphol to the national borders without the flight crossing built-up areas.
An aircraft cannot fly a ‘zig-zag’ route that avoids built-up areas. This is partly to do with limitations in the navigation systems and with safety and efficiency requirements. In practice, therefore, the flight routes consist of straight paths, connected by more or less circular bends. The number of bends is limited here. Efforts are made to fly across thinly-populated areas as far as possible. The routes from the Polder runway are an example of this.