Single phase energy meter measurement
Instantaneous Volts multiplied by instantaneous Amps is true power and no compromise and when micros implement this they are doing it exactly the correct way.

VI x power factor may not be true power because hardly ever is the voltage waveform or the current waveform truly sinusoidal and only when V and I are truly sinusoidal can RMS Voltage multiplied by RMS current multiplied by power factor = v(t). i(t).

Here are several examples of voltage and current waveforms shifted in phase to each other: -



The first picture is when v and i are in phase and power is maximum. Note also the example when v and i differ by 90 degrees (bottom left) - power is zero (as you would expect) but, if there is any harmonic distortion, VICos(phi) will be inaccurate.