Storing a lot of energy and delivering it faster are two separate problems. The batteries you linked are design to store a lot of energy, but are only rated to

Storing a lot of energy and delivering it faster are two separate problems. The batteries you linked are design to store a lot of energy, but are only rated to deliver it at 30Amps. Cranking even a medium sized sedan would take 5x that or more. Creating something that can do that reliably requires a lower energy density. LiFePO4 by itself also doesn't stand up particularly well to cold temperature. The capacitors do most of the heavy lifting involved in starting the car. Using the combination of the two also enables some other nice things like the dead battery prevention.