The RC guys use LiPo battery cells. I believe they run them without battery management systems (
BMS). LiPo's usually have much higher "C" or discharge rate than LiFeP04 cells. As you say, the LiPo's have 30C and 40C discharge rates, compared to LiFeP04 rates of around 2C. This means that LiPo's can produce
much more current (amps) for a
much shorter time.
For example, a 10AH LiFeP04 battery at 2C will provide 20A nominal. The same 10AH LiPo battery at 30C will happily provide 300A, if you can use it. If you're running a MPII, rated at 30A, there would be a noticeable boost in performance - not so much as the 300A figure would imply, but probably better than 50%.
The controller is rated at something like 45A. If not restricted, and under heavy load, the motor may draw as much as that, although I've noticed my motor seldom draws more than 30A, even climbing hills.
The downside to running LiPo cells, without
BMS, is the potential for fireworks. Those RC boys keep a careful eye on their cell voltages, which is pretty much what a
BMS does.
So you see, it's not a "battery response time" parameter, but a "current available" parameter, which we call "C".
JeffDennis; what's "bloviating"?