> Wouldn't it be easier to just use an ammeter?

When the load is not simply resistive, multiplying RMS amps times RMS
volts will mis-estimate actual power consumed, sometimes drastically.
(For example, if you have a purely capacitive or inductive load,
current will be 90 degrees out of phase with voltage, and power
consumed will be zero, even though current is flowing.  Power consumed
is the integral of instantaneous current times instantaneous voltage;
with an inductive or capacitive load, RMS volts times RMS amps will
overestimate actual power drawn.

Now, when the load is a switching power supply, current drawn consists
of a spike at the peak of each voltage half-cycle, rather than anything
even close to a sine wave.  In this case, actual power is something
more like RMS amps times peak (not RMS) volts; measuring the current
and multiplying by the nominal voltage will *under*estimate power
consumed....

Or, of course, I could be burbling nonsense.  Any power engineers here?

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