To put it in layman's terms, caps can be considered a bandaid for less than optimal power wiring.
If you had too small of a power wire setup, or a poor ground where the supply wiring was current limited, the capacitor would step in and provide the instantaneous current/voltage to prevent the voltage sag that would go with a big bass note hit.
If your wiring was correctly sized to the amplifier, with a good solid ground connection, and if you had a good battery with solid clean connections there, the capacitor is to a large degree unnecessary. A properly designed power wiring system basically prevents the need for a capacitor as the properly designed power system provides the current and voltage that a big bass note needs. That is the very short and sweet of it.
There are going to be exceptions to this set of parameters I have pointed out; there always are.... For example, for some car installations where the power wiring is totally proper, some folks will experience that headlight dimming, but others will not. Those point ot differences in alternators, charging systems, relative system needs, amplifier power, etc...
As always, my explanations tend towards somewhat of a simplfication in order for the largest audience to grasp the concepts presented. It is rarely a totally-enveloping answer that addresses all tweaky little minute exceptions...
But to the bottom line, for a properly designed and installed system, most people will find capacitors are not necessary for proper electrical function. It is often just a nice touch of bling some folks decide they want to add...
David, care to elaborate?
Phil
Kicker