A Tesla S has an 85kWh battery. To charge that in 30 seconds requires 10,200,000 watts of power - approximately the full electrical service to a decent size skyscraper. That's 42,500 amps at 240V, the full maximum power available to over 212 modern homes and a totally impractical amount of current to handle with any reasonable electrical equipment. So while fast-charging batteries are great and a necessary step forward in technology, the universal adoption of electric cars will require not just upgrading our infrastructure, but a complete rethinking and redevelopment of the electrical grid using not-yet-imagined technologies.
It could also be a grid engineer's best friend. You just have to change the way you think about it - the cars would be a *massive* local storage resource. The VAST majority of people are just going to be plugging their cars in overnight at home, and starting with a full "tank" every morning. I could imagine a system where, once electric cars are ubiquitous, most parking lots and cars would be designed so that when you park, your car just automatically gets hooked into the local grid. You set some parameters on the car for min/max charge levels and buy/sell price limits, and suddenly you don't have to worry so much about demand spikes. Demand goes up, the price/kWh goes up, and once it starts passing the "sell" threshold of the local automobile population, they start discharging into the grid. You just tell the car "keep at least X% charge so I can get home." If I show up nearly empty, and there's 1000 other cars in the lot mostly full, they could charge mine without ever making demands on the grid.