Who says you can't reinvent the wheel?

I think everyone has missed the obvious because its too simple.
Energy can be stored in the rotation of a mass...a wheel. The amount of energy stored is proportional to the mass and the square of the velocity (which depends on the diameter). Its Kinetic Energy only going around in circles. Flywheels are as simple as it gets: One moving part! To negate the adverse gyroscopic effect, two counter-rotating flywheels could be used. Just "plug it in" and it winds up. With motor/ generator coupling, regenerative breaking is the obvious choice. And you're right: the distribution system is already in place. Every lamp-post becomes a refeuling station. On the downside: it will fly apart if it becomes unbalanced so proper containment in the event of a collision is a highly recommended.
That's my choice for the way to go in personal transport.