You can have real or apparent power on phase 1, but you can have only apparent power on phases 2 & 3 if you use the standard (single-phase) sketch. Real power will be correct for phase 1, but wrong by a factor of -0.5 for phases 2 & 3.
The 3-phase sketch assumes the phase voltages are reasonably well balanced, which will be the case if your supply has a sufficiently high fault level. The loads need not be balanced. If the voltages are not balanced, then there will inevitably be errors in the power calculations for lines 2 & 3.
If everything was always accurately balanced, you would only need to measure one phase, then multiply by three!