I never said the home would be the primary charge point, you wouldn't charge like this at home, but at a charge station.
I'm implying that these are the specs necessary for an electric car to truly be taken seriously as a replacement for a gas vehicle.
Furthermore, charging at a higher voltage, say even 720 volts (about twice the current roadster's voltage) gets you down to 500 amps to charge a Tesla in 10 minutes, which is manageable for cables. Charge stations could have a reserve/buffered system they can charge from that way they wouldn't be hitting the grid all at once if 5-6 cars show up. You could do a similar thing at your house (basically a large UPS)
Even a 1 hour recharge is not bad. After driving for 350 miles, I wouldn't mind stopping for a nice lunch. While you're having lunch, the car's batteries get recharged, for much less than the price of the lunch.
The cables would be as thick as your arm.
You can do battery swaps instead, but it requires an infrastructure build out first.