If a meter truly measured instantaneous power, then even for the most steady load possible, you'd get a different read-out depending on where the waveform is in its cycle, at the time your meter samples. Measure at the peak or trough of the waveform, and get the maximum power that is theoretically twice the average power. Measure at the zero crossing, and get zero. It would either have to time-average, or sample at specific points within the cycle and extrapolate through the assumption that it is a sine wave.
Whether it does this by time-averaging, or whether it does this by extrapolating the waveform, it still most likely would give you a cycle average power rather than a truly instantaneous power. The cycle average power is the more useful information to most users.