Additionally, being giant batteries, electric cars have the means to charge when most advantageous to the national grid. Most electric cars already have an option to wait to charge until off peak rates happen. (Off peak rates being cheaper because low overall demand.)
But electric cars may be useful to the grid as giant surge protectors for things just like that cup of tea electric kettle break. Under some of the "smart grid" proposals, the electric companies would be able to not feed electricity to a vehicle in those brief moments of high demand on the grid, prioritizing immediate needs like people's kettles. Furthermore, "smart grid" ideas could even use electric cars as battery backup options, "leasing" already stored energy back from the car and paying it back later, as changes in demand happen.
Even if some of those "smart grid" ideas don't get nationalized, you could still theoretically take advantage of some of those kinds of things in your own home.
So if anything, electric cars may be surge stabilizers rather than surge causers.
The grid would prefer a another demand curve, so overnight charging is helpful.