did you read the opening and also the last sentence in my first post in the linked thread ? Batteries for what other than portable players and amps would I post about here ?
Actually current/power capacity of the battery is exactly what I am NOT talking about. Its already ample. Adding too much capacitance has its own problems also.
This is about ac impedance of the battery. It is analogous to power supply impedance.
And it is about the current spike delivering capability of the battery(internal resistance). Music could have as much as +12db spikes, the amp and the power supply(battery in this case) should be capable of meeting that current demand - without any drop in voltage. Dont mistake this for "capacity" (like mah) of the battery. Chances are a 1000mah battery might be able to provide better current spike than a 2800mah battery.
Btw, power supply ac impedance is the same issue that you would run into if you used too much psu filter capacitance (>2200uf typically). So adding capacitance also works only upto a certain point.