If every house ends up with a solar array and an equivalent of a Tesla Powerwall (other brands are available) then there won't be massive demand on the grid.
You don't have to fast-charge a Leaf. You can charge it overnight.
I pay for a "100% renewable" electricity tariff. Of course not all of the energy I draw is from renewables, but it is all reinvested in renewables.
If people continue to adopt EVs, adopt renewable tariffs, and adopt self-generation and self-storage, everything will be fine.
No, an EV is not as green as a bike. But have you ever tried getting furniture from IKEA 60 miles across country on a bike, with a baby and toddler in tow?
Disclaimer: avid cyclist (6 miles a day to commute) and EV driver since 2013.