How can you do that without a special electric meter for the car to avoid hitting people who rely on electricity for heating (old economy 7 & new heat pumps)
Only way would be to mandate car charging at a different voltage & then meter that voltage output differently from normal electricity.
Same with this road pricing stuff. Are they going to factor in the kerb weight or MPG numbers to weight the charges so heavier / more polluting vehicles pay more? I doubt it - thats why all those SUV tank drivers think its much better than tax at the pump
Not exactly hard is it.
e.g. Give people with storage heaters/heat pumps a rebate that covers heating costs.
Your second point about kerb weight explains nearly why the electricity should be taxed.