The issue is that mains power is not a pure sine wave(*) so that to measure true power you have to take account of the waveform, hence the desire to sample the waveform that frequently. If you only want a coarse measure of power you can take short cuts with this.
What I was trying to say is "integrate the product of V and I over unit time to get average power"
(*) in these days where most mains appliances have switching power supplies (even microwave ovens)