One of the great things about concierge medicine (also called direct practice) is the ability to contact your doctor at any time. Also, that your doctor will work with other caregivers and advocate on your behalf.
Yes, it costs you extra for the extra service, but that is how the doctors can reduce their case loads and free up the time to provide you with additional attention. Not everybody thinks the additional fee is worth it, but many do. Plus an argument can be made that the customized care saves money by reducing duplicative tests and hospitalization.