Setting side effectiveness, expense, and weight concerns, I’m unconvinced this is “…definitely illegal…”
There are some legitimate safety concerns regarding the safe storage of energy, safe discharge of the capacitors, and the impact of cycling those capacitors. But storing energy isn’t illegal. There’s a potential question of whether or not the capacitors could be charged prior to the match under R46, but this is electrical energy, so I would contend R46 doesn’t apply.
The presence of a large capacitor complies with all the rules cited above:
R39: Energy stored in the capacitor would still come from the battery.
R47: The implementation of a capacitor as described by the OP does not require alteration of the pathways described here
R61: A bank of capacitors can be purchased COTS
R63: Presence of a capacitor bank on a branch circuit protected by a circuit breaker does not alter the described power pathways.
Take all that together and consider such capacitors a “CUSTOM CIRCUIT” and the concept is legal. The implementation is where a team could run afoul of the rules.