For cars any fast-charge battery doesn't remove the *ahem* "current" stumbling block but rather *moves* it.
Tesla's fast-charger claims a 4-hour recharge on a charger pulling 16.8kW and a charge will get you rougly halfway from San Francisco to LA - a trip easily made on a tank of gas.
To match a gas-station fillup you would need to transfer that amount of energy in about 5 minutes requiring a supply of a touch over 800kW. At 600VDC - the voltage used by BART - your cables would *only* need to carry about 1,300A to the car. By my reading, this means approximately six "strands" of 0000 wire per conductor or a dozen for a two-conductor cable. That cable will weigh approximately 6-pounds/foot plus an undoubtedly hefty plug and it will still get pretty warm during charging as well as being enormously attractive to copper thieves.
But since the fuel-powered vehicle gets 2-3 times the range on that refueling a more realistic comparison requires you to at least double the above numbers to reach refuel-time/driving-range parity. If they don't double the range on the electric vehicles then you need double the refuling stops with the attendent increase in number of "pumps" or stations. The required energy needs to get to the vehicle somehow.
When I pulled into Costco to fill up there were 20 pumps all with cars at them. Even if only half were actually fueling, the station would need an 8,000kW feed before even factoring in burst and safety-factor requirements.
To make matters worse, most people refuel in the daytime when electric loads are highest. Of course this is offset somewhat by the fact that daytime is when solar is available.
Overall, high-speed recharge for cars may bring as many or more problems than it solves, especially when the battery-swap alternative allows for load-leveling, for leveraging the ability to purchase at the cheapest or most environmentally friendly times, for eliminating the need for an owner to worry about large battery-replacement costs and potentially even for returning power to the utilities at peak-demand times.