There are some power companies that have tariffs that incentivize EV charging when demand is low.
This can done with a simple timer or it can made automatic resolving to variable prices on 30 minute time slots if a suitable smart meter is used.
Given the energy crisis in Europe, this kind of peak demand reduction is going to greatly encouraged.
Such innovations don’t need changes to the grid. Demand limiting has been around a long time for large business customers with high energy demands. It will simply downsize to become available to domestic customers. People like cheap.
There are also Vehicle to Grid pilot projects but that requires bi-directional chargers.
These could save the need for a power station or two.
Grids are designed to cope with peak demand. There is a lot of spare capacity available outside of peak times. EV charging patterns, where charging can be done at home, are very different from the routine of filling up an ICE vehicle at a gas station. EV charging facilities needed for long distance trips can also use batteries that can be charged at cheaper rates at times of low demand.
It is still early days with EVs and all the charging infrastructure technology.
Are there any dire warnings about EVs from grid operators that are credible?
Grids have bigger challenges coping with renewables. They need more wires. But that is a different story.