This seems to work well when 95% of cars are still ICE.

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.

I wonder how well this works when some (many?) people don’t move their cars for days or weeks as a time.

That's not a huge deal either, really. In time, more and more parking spots will have charging ports. The fact that they aren't all used all the time will actually make it easier to manage the grid loads.

Imagine you park your car and let either the car or the charger know you aren't moving the car for 2 or 3 days. It can use that knowledge to delay your charging until local demand is lower, or power is cheaper.