But that way there would be no way to compare cars, because the "fuel efficiency" would depend on the charging station. And it would be even more ridiculous in countries that produce all electric energy with renewable energy (e.g. Norway), because the car would always display zero, no matter whether it is a efficent car or the electric equivalent of a gas guzzler.
For cars that produce CO2 themselves, CO2 emission might be a good metric. For all others, it isn't.
The best way to measure efficiency would be something like MJ/km. The only one people care about is €/km (or $/mile or something similar).