Why, if you're in a dead stop in a rainstorm, would you leave the headlights and wipers on?
In an EV, you'd have to shut down the car sooner or later, just as you would eventually have to in a gas-powered car. If (or probably when) EVs become popular enough, there's nothing preventing the construction of an emergency charge assistance truck even today. Just stick a bunch of batteries in a box truck, probably along with other roadside emergency equipment. That part's pretty straightforward.
I don't think there's any electrical battery technology that comes close to diesel's energy density (35.8 MJ/l). Lithium-ion batteries, according to Wikipedia, are 0.9 - 2.63 MJ/l; it's possible that may be outdated information, but it's still at least an order of magnitude lower. I'm not sure it's really all that necessary to match the volumetric energy density, though; there's no reason in general why an electric vehicle can't have a battery bank that takes up more room than the fuel tank on a diesel vehicle. Some space is certainly saved by the simpler drivetrain (an electric motor drive is smaller than an engine and transmission and needed engine accessories). Other space not readily usable for a fuel tank can be used for a battery bank, as there's no need to worry about such details as plumbing and arranging it so that the fuel can be used.
(There are some very long distance high speed EV's in use around the world already, by the way, that run on rails. One way to get around electrical storage difficulties is to run wires....)
