We can do the battery storage right now, it's just not as great as what we'd like.
If you switched all cars over to electric tomorrow, the grid would melt down in every country that attempted it. There is not even remotely enough power available to handle it. Most first world countries are running their national power grids with a very modest buffer (and for countries sub first world, forget about it, they're still dealing with routine rolling blackouts).
By the time all autos are switched to electric in 30 years, hopefully self-driving cars have wiped out at least half of all vehicles in the first world.