Is there an advantage to beta-vs-Ic flatness in BJTs?
Let's pick a random audio power amp schematic from google images...

Output transistors (OPT) require base current Iout/hFe.
This creates a corresponding voltage drop on base resistors R25, R28 ; also the Vbe of the driver and predriver transistors (if any) will vary a bit according to OPT base current. This creates a voltage drop between the collector of Q4 and the output voltage which depends on Iout. Also, loading on VAS output (Q4 collector) depends on pre/drivers base current which depends on OPT base current.
If hFe gets lower at high current, then OPT base current will increase in non-linear fashion as output current increases. This creates a non-linear voltage drop between VAS output, and draws a non-linear current from VAS output. Both of these increase large signal distortion.
If hFe is constant, output transistor base current is proportional to Iout, therefore its effects on the preceding stages is linear.
TL/DR: power transistors with flat hFe vs Ic reduce non-linear loading on preceding stages at high current and thus produce lower large signal distortion.