Peak loads let the grid collapse. Not constant loads over N hours. If everyone starts charging their EVs at roughly the same time (like when getting home from work) it won't matter that the EV uses less power over 24hours than a space heater.
EV zealots are just blind to the issues their silver bullet creates. Just like the "walk-able cities" folks.
This is why we have different pricing for different hours. Only those that actually need the capacity will use the expensive power from 16-20.
Others will use dirt-cheap night time electricity.
And with Vehicle to Grid smart people can sell the extra energy in their car battery during peak hours and use the credits from that to charge their car overnight.
None of this is some kind of magical tech that's hard to use. Gridio (https://www.gridio.io) already exists and works directly with multiple EV brands.
EV zealots are just blind to the issues their silver bullet creates. Just like the "walk-able cities" folks.