Local generation can take up the slack too, with fewer volts being sent over wasteful energy grids - that can waste 6-7% of energy in transit, up to 30% in undeveloped countries.
I was concerned before I got my first electric car that the electricity bills would be massive. But I use the car every day, charge it at home 70% of the time and I have hardly noticed an increase in my bills.
I think the fear that the grid won't be able to cope is overblown. Especially in hotter countries where solar will have such a massive impact on transport.
In fact reducing oil consumption will only have benefits in remote locations where oil is very difficult to come by. Think about places where oil is a reason for war. No one will fight over the sunshine.