Nobody sane produces electricity on anything but the most minor of scales using it
At the moment. But your scenario assumes that most of transportation switches its energy source from petrol/diesel to electricity. That implies that the demand for oil will drop through the floor. And that implies that oil will become very cheap. Which in turn implies that it will again start to make sense to burn it to make electricity to recharge the car batteries.
Remember that electricity is not a source of energy. To support your case for nuclear you need to show that coal and hydrocarbons will be unable to support the energy needs of the humanity in the near future. Whether cars run directly on hydrocarbons or whether there is the intermediate stage of electricity involved does not matter much for this issue.
Oil has uses other than automotive fuel - way before it reaches the point where it becomes competitive with coal or uranium for stationary power plants, demand from the plastics, avionics and the petrochemicals industry is going to put a floor on the price. I don't expect the saudi oil to stay under the sand, but as an energy player, the global oil industry is doomed. Coal is going to be raking in money hand over fist for a while as prices spike, but once a transition to fission starts, - and high coal prices will get that started - they are done for too. King coal only still reigns at all because the world has been collectively insane about fission due to living in the shadow of the atomic bomb.
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.