You could do that, but energy density is the key metric here. Energy density determines the size of the battery required to store a specific amount of energy.

You could do that, but energy density is the key metric here. Energy density determines the size of the battery required to store a specific amount of energy. There's only so much space in the car, and you also have to factor in that any battery that will be moved by its own power loses efficiency with lower energy density. You've got a huge battery to move, and physics dictate that accelerating this battery is going to use more energy. So, let's say you split this hybrid battery 50/50, your quick charge-discharge battery quickly becomes too small to deliver meaningful range, and you've given up space that could be used for the traditional battery.