What would the output impedance be if R5 And R6 were not in the circuit?
Without the emitter resistors, the output impedance (and other characteristics of the circuit) would depend very strongly on the specific characteristics of the transistors, which can vary widely even among transistors from the same "batch". The resistors are used specifically to reduce or eliminate that dependency.

Instead, there are other ways to reduce output impedance, such as increasing the open-loop gain of the circuit and then applying negative feedback directly from the output terminal.