Why are BJTs common in output stages of power amplifiers?
To make an Audio Voltage source, you want the crossover voltage distortion to be null which requires some quiescent DC current > 1% of the max current. This modest distortion and output impedance is reduced further by negative feedback or excess open loop gain.   The active diode bias DC voltage can be predicted in mV for the differential Darlington output stage.

However for MOSFETs the conduction threshold can vary 50%  e.g. 1 to 2V or 2 to 4V, so the biasing for cross conduction to eliminate crossover distortion is not easily done with low voltage gain linear power amps.  

Edit May 22:
Also, Thermal Runway exists as stated by @Thor from the micro-array FET structures sharing-current with Vgs NTC effects in linear mode yet PTC effects for RdsOn in full conduction mode.  Without proper transistor component selection, this can result in catastrophic failure.