I manage the warranty department for a large homebuilder and while we DEFINITELY do not live in A/C country, I'm going to use the principles of winter heating to explain it. Modern high-efficient HVAC systems are designed to actively pull fresh air into the building envelope and actively duct interior air out. Also, whether heating or cooling, the system responds to whatever temperature is read right at the thermostat location, not talking other areas of the home into account. Running the fan constantly (which, by the way, it is designed to do - it is a variable speed fan which self-adjusts to minimize wear and tear) provides much more even heating and cooling to all rooms and improves the quality of indoor air by exhausting humidity and catching contaminants in the filters. Today's homes are built "tight" for energy efficiency and without active ventilation you essentially live in a zip-loc baggie. Electrify usage does come into play but should be minimal given efficient design. Some old-school HVAC contractors, more familiar with past mid-efficient systems (which don't work the same way) might advise against running the fan but we believe that to be a mistake. Bottom line - operate it however you want, but it really is designed to be optimum in the "on" position.
P.S. Changing/cleaning the filters regularly is the single, most important aspect of minimizing wear and tear on your fan motor and maximizing your indoor air quality. My company voids warranty on furnaces if we find the filters to have been neglected.