It would be nice if the battery had multiple outputs: for example, connect the capacitor to just the starter motor and have a second output for everything else.

It would be nice if the battery had multiple outputs: for example, connect the capacitor to just the starter motor and have a second output for everything else. This way all the lights in the car would not dim during starting (why should the electronics have to deal with brown-outs?). Diodes could be used for the charging current input.