Advice needed for split core clamp-on power monitoring circuit
You haven't said anything about the loads to be measured or the accuracy required so I'll answer generally.

Picking up on what you said about phase difference: measuring power is not this simple as you cannot assume a sinusoidal load current. Any switching power supply will switch at least in the 10s of kHz with important harmonics more than 10x higher. In other words, it isn't "only 60Hz". You can sample with a CT optimized for low frequency, but your result may not be anything near what usually passes for "True RMS".

The phase difference between the voltage and current is only useful for simple power factor calculations with a sinusoidal load current, typically found in an inductive load like a large motor. With any non-sinusoidal load current it doesn't matter so much. Power meters sometimes report it separately from power factor, calling it "displacement power factor" or somesuch.  From a noisy switching load you can see a "displacement power factor" of 0.95 or so but a real power factor of 0.50. That shows you how misleading it is by itself.

What you're proposing can give perfectly usable results, it all depends on your specification.