The ongoing growth in global electricity demand and rapid proliferation of electric vehicles (EVs) are posing challenges to the operation of the low voltage power networks and their components. This study aims to analyze the impacts of peak-load demand on the distribution transformers, considering mild and extreme combinations of electric energy demand and localized charging of plug-in EVs under their different penetration levels, hypothesizing that shifting the demand for charging throughout the day can reduce the aging of distribution transformers. The proposed method employs a fuzzy-logic-based tool, which incorporates the influence of ambient temperature, higher harmonics, reactive power compensation, reverse power flows, and overload. Three different charging/discharging modes have been considered: demand charging, off-peak charging, and synergy of off-peak charging and vehicle-to-house technology. The results indicate that off-peak charging emerges as 2.1 times more effective than demand charging in terms of the transformer's loss of life, particularly for ultimate EV penetration of 100 %. It is demonstrated that the utilization of charging scheduling for EVs should be prioritized to defer costly system upgrades and reinforcements, particularly when EV penetration exceeds 50 %.