Energy is proportional to the square of the electric field. That the average value of the electric field is zero doesn't mean the electric field is everywhere, always, zero. Nor does it imply that the variance of the electric field (which is what the average energy is) also vanishes.

The expectation value of the electric field is zero due to rotational symmetry-a non-zero value would indicate a particular direction in space (which could occur if the source weren't spherically symmetric, for instance).

#Stam_Nicolis

Thank you for your informative explanations.