So coming home putting the 7kw EV on charge isn't a peak load as much as putting the kettle on at 3kw and the oven on at 4kw??
No because the vast majority of us have our EVs programmed to start charging at 12.30am when demand on the grid is very low and actually the grid needs load to stop peaks in voltage.
The way the car starts charging isn't a sudden rush of current, they gradually ramp up charging rate. This is very much preferred way for the grid.