Emitter follower amplifier becomes relevant when working with very low HFE high power transistors. in this example the main output npn transistor has a hfe of 3 (it's reversed because the minimum hfe in EC is 10, but this circuit simulates the same effect so ignore the reversal and pretend it's the right way around).
with a hfe of 3, to get 6A through the collector-emitter, the Transistor will need 2A of drive current through the base-emitter junction. if the transistor was arranged as a common emitter, that 2A would be sunk straight to ground and lost. the emitter follower arrangement allows that drive current to flow through the load, providing a total of 8A