Why would it not work with 100% EVs?

Because the cables that deliver the energy would then burn through.

Cars don't actually use that much power relative to the amount that households already use if they're not fast-charging (using power here in the technical sense (amps) not as a synonym for energy (watts)). Smart charging meters that default to a cheap off-peak slow-charge (i.e. an overnight charge) with the option to override with a fast charge for a premium will probably solve 90% of our problems here.

Or get nicked.