What's wrong with variable bias?

Looking at the schematic, the TA-A1ES switches the quiescent bias current from low to high depending on volume output. At low volume it uses low bias to save on heat output from the output transistors. Both halves (both NPN and PNP output transistors, ie, + and - halves) of the push-pull output stage are kept conducting in such an arrangement so crossover distortion is kept to a minimum. The output stage is still operated in class A at low volume, as the bias required for class A operation for high volume isn’t needed at low volume.
There is a slight advantage to distortion at low volume when the output transistors are operated in high-bias class A all the time, as in traditional, hot-running class A amplifiers.
Note that nowhere in the TA-A1ES literature does it claim to operate in class A, instead saying it has a Smart BIAS system. My Denon POA-4400 designed in 1989 has what’s called Optical Class A which operates in a very similar manner to the Sony.

lostrak, In class A both output transistors operate all the time. Current thru one transistor is equal bias current plus half of the load current, while current thru other transistor is equal bias current minus half of the load current. Because of that linear range of output current is from -2x to +2x bias current (-2IB < IL < +2IB). Adjusting bias current lower will reduce power losses, but also will limit output current. Predicting ahead of time magnitude of incoming signal might be difficult while transistors will be forced to operate in less linear region.

Class AB with adjustable bias is not the best either. In class AB feedback has to be much deeper in comparison to class A (to reduce nonlinearities), so the damage is already done (TIM), while switching between classes switches also amplifier’s transconductance (input voltage to output current gain) since in class A two output transistors work and in class B only one. This will also add distortions.

My Benchmark AHB2 is a class AB amp with non-recursive feedback (separate error amplifier) and adjustable voltage rails (class G and H). They obtained AAA (Achromatic Audio Amplifier) patent from THX Ltd. (George Lucas). This itself reveals how difficult is to design such thing.