Are the aerogels used in supercaps still highly insulating, or are they filled with another dialectric material that would conduct heat? The reason I ask, is that I'd imagine that capacitors could be made in plates (instead of rolling them up into cylinders), and used for wall materials. The metal conductive layers would block moisture and the dialectric aerogel layers would act as insulation to keep heat in the house.
Interestesting idea but i would think thrice about living inside walls which could discharge humongous amounts of energy in seconds. But i bet the visuals might be awesome. NSI (Not Snark Intended).
Your walls could also store electricity.