The booster wasn't just about energy storage, To add to what
@Tony73E wrote... (And correct me if I am wrong)
The booster (thinking here the original SR CC1&2/class 70's) was a motor generator set (MG) which took the 650v supply from the 3rd rail and output an isolated variable voltage, roughly -ve650v to +ve650v with respect to the conductor rail voltage. (In reality I think it was more like 600v + and -)
This voltage was then connected in series with the conductor rail supply and applied to the traction motors. This means the traction motors are energised at a variable voltage from ~0v (-ve 600 in series with +ve650) to ~1200v, (+ve600 added to +ve650). Because the variable voltage is derived by modifying the field current and polarity of the generator in the MG set losses are reduced, as there is no longer a need for starting resistances. The traction motors are wound for 1200v DC. Because the MG set is only supplying half the rated voltage at the rated current the booster MG set only needs to be rated at half the installed horsepower of the traction motors.
The flywheel was then added to maintain power over gaps in the third rail. I have read reports that when motors were running at a low voltage (say 100v) for starting the gap could give a situation where instead of +100v on the traction motors you suddenly get 550v as you pass over the gap. I am not sure how this was managed in practice.
Its also worth remembering this system was developed by the Southern Railway well before any sort of power electronics were available for traction motor control, not even semiconductor diodes. A similar system was then carried forward into the 71's and 74's