If large numbers of people have EVs, that could potentially cause issues for balancing the grid (which is going to become increasingly more challenging anyway).
But it doesn't have to.
The real game changer will be bidirectional charging (cars and chartering points aren't set up that way yet).
Take power from the grid when demand is low and prices cheap. send it back when demand is high or when supply is low (for a financial incentive).
(Or, if you like, don't because I am sure no-one will force you to charge your car when its cheap).
But if a large number of people have EVs, there is an opportunity there. The way we pay for and use electricity is going to change over the next few years, and if that seems impossible to imagine, then think back to how you used to pay for and use telephones (as an example) in the 90s. One land phone, internet on dial up, phone bill with every call charged for. Huge changes.
Problem is though that a number of different interconnected technologies need to be developed, rolled out, improved etc. And that is hard, when each technology really needs the others to be in place first before the benefits can be seen.
(Btw, I earn my living in the oil industry si I have NO personal incentive to big up renewables and EVs. But I think change is coming and its fascinating).