After more searching it seems like the 10000 Farad super cap invented by Sunvault is still a pipe dream. However Maxwell has available a 3400 Farad 3V cap. Also, Skeleton a German company has announced they are coming out with a 5000 Farad super cap in 2023. So I played with some numbers:
Supplying 12 kW for 15 seconds is 0.05 kW-Hr which is 180,000 joules. A 16S (48V) pack running a 24V motor with a voltage drop of 24 volts can supply 184,000 joules. A 20S (60V) pack running a 36V motor with a voltage drop of 24 volts can supply 196,000 joules. A 23S (69V) pack running a 48 volt motor with a voltage drop of 21 volts can supply 182,000 joules. The Maxwell caps are $50 each. From what I have seen more expensive than LTO batteries but they can discharge and recharge really fast.
Can the ESC's that are being evaluated deal with that much voltage drop from the power source?