The charger itself is basically just a fancy power switch.

Cutting power to It won’t harm the car.

No, since the power electronics and on-board charger on the car are designed to handle sudden power cut.

What in practice happens is:

• EV notices the power pins are not energizes, the actual charging electronics and battery is designed to handle this
• Upon the wall Electric Vehicle Supply Equipment (“11kW charger”) losing power, its based to open contactor springs open. The EVSE must provide constant pilot signal to its contactor (big fancy relay switch) to keep it closed and thus power pins energized.
• Also the power to the pilot signal sent from the EVSE to the car is cut, since the control circuit goes powerless. This will cause the EV to cut its own pilot to its internal contactor, isolating the connection double. Since no pilot from the wallside is one of the safety conditions of “Something abnormally, cut connection”

Ao charger will just suddenly lose power, but that is not a problem. Both the wall supply equipment

For what it’s worth, I cut the power when charging my ev everytime because I want to charge only between 22h00 and 6h00 (when power is cheaper). I’ve done that for more than 2 years now and never had any problem nor did I see a downgrade in the autonomy of the battery (peugeot e-208).