What are some applications where full AM is used nowadays? Is it used at all considering the fact that it is less power-efficient than, say, AM with suppressed carrier?
AM is still used worldwide in civil aviation, where there is a large installed base of radios (in small planes, etc.) than can not be easily updated (due to multiple national and International regulatory hurdles), and where you want one transmission to be able to talk over another signal on the same channel in an emergency.
AM radio receivers are simple and cheap using primitive technology (1 discrete diode, etc.), and there are still a few parts of the world where people can barely afford an old one of those.