Hysteresis and eddy currents

Hysteresis would also lead to harmonics, complicating things even further. And, when considering unbalanced three-phase systems and/or the presence of harmonics, the conventional tools for power system analysis might not be applicable.

The losses due to hysteresis are limited by using better materials in transformer core. Eddy current losses are limited by using laminated construction. These losses are a relatively small portion of the total losses in a power system. Most of the losses are Joule losses (currents and resistances).

Because "energy" might be misinterpreted. Sure, reactive power is associated with charging and discharging (actually, charging with the opposite polarity) magnetic and electric fields. So, electromagnetic energy "flows" back-and-forth in these fields.
But they do so twice (one positive, one negative) on every cycle of the AC system, so the average energy is zero.
There is an energy "exchange" between magnetic and electric fields. But no, that is not an oscillation in energy (kWh), not something that you could measure, for instance, in the torques on a mechanical shaft (that is purely kW, active power).