Re: Facts and figures?
"Also, if it's that good, why not replace the entire battery with a lump made form this 'super capacitor' material? ."
Because if you can make panels you already need for structural and aerodynamic reasons into power storage, then you don't need a separate battery, reducing the overall component count, assembly complexity, and total weight. You may also have other disadvantages of assembling as a single "battery", such as heat losses in charging and discharge that aren't a problem with a large surface area. Indeed, if your energy is more widely distributed, then any point failures would not be as exciting as a point failure on a single energy storage brick.
If you think about how (for all the challenges) the 787 is revolutionary for aviation in terms of construction and performance, through the use of CF and different approaches to electrical systems, and consider how that might change car making. Does it really make sense to make car bodies out of metal at all, with the all the necessary rolling, bending, punching, welding, corrosion protection? And if you're asking such fundamental questions then you'd question why you have so many different components, which can be eliminted, integrated into other parts, or made differently through smart tech. Could you ultimately 3D print a car body? I'd have though so, and a better, lighter car than we currently make with steel origami. Could you print the car round the drive train, or pre-assembled interior? Maybe. Could the panels combine solar charging with energy storage? Certainly, though it wouldn't help us much here in the UK.