What is the function of series inductors on the motor phases of a commercial brushless EC/BLDC motor controller?
The inductance is present to smooth the phase current. If there was no inductance in the motor at all, the phase current would look like the PWM voltage waveform. This would cause excessive eddy current losses in the core, potential EMC issues, and will also reduce overall torque production efficiency, as the torque output is the average of the current waveform, whereas the resistive losses are the RMS of that same waveform.

In most motor designs there is sufficient inductance present in the motor anyway, but if the PWM frequency is low, or the motor is a coreless design, then external inductance may be required to sufficiently smooth the current.