If you're really comparing capacitors favorably to batteries for "a steady flow of power", then it appears you're also talking crap about something you know nothing about. There is no comparison at all between a battery and a capacitor in terms of how much steady current they can provide. This is incredibly easy to see for yourself: take a headlight bulb and connect it to a charged capacitor. Time how long it takes for the bulb to go out. You'll find that the capacitor is completely discharged in a matter of seconds. You won't have to bother doing the same test by connecting the bulb to a battery; obviously the battery can provide steady power for a much, much, much longer period of time.
Now, from reading your post it seems likely that you, like many others, think the battery is the main source of power for the vehicle electrical system. If that were true, then capacitors wouldn't even have a theoretical benefit, because a capacitor does not create power. It can only store it. It can never hold a higher charge than the voltage source it's connected to, nor can it have a lower charge than the voltage source it's connected to. The instant the capacitor drops below the battery's voltage (which would happen as soon as any load is placed on the cap) current begins to flow from the battery to recharge it. So the cap might as well not be in the system, since the battery can hold its charge for a much longer time than the cap can under any load.
However, the battery is not the main power source for the system. While the vehicle is running, the alternator is the power source. This is where the capacitor, in theory, becomes a benefit. The alternator produces a higher voltage than the battery, and the capacitor can charge to that level. So the battery doesn't provide any current at all while the engine is running, until the point where so much current is being drawn that the alternator reaches its limit and its output voltage drops. Once the voltage level drops below about 12.8 volts, the battery starts to discharge. So the benefit of the capacitor is that it can release its stored charge after the voltage drops below what the alternator usually provides, until the point where the battery starts to discharge. Once the battery begins discharging, the capacitor has used up its benefit: it CANNOT produce current at that point. It becomes useless, and if the load doesn't change, the battery will eventually drain.
The capacitor may have some benefit for the amplifier in this case: if there's a sudden, very brief demand for current beyond what the alternator can provide, which doesn't last so long that it drains the capacitor and the battery has to take over. Remember that a capacitor doesn't really store very much power! If the demand on the alternator continues for any length of time, the capacitor is useless. We're talking about lengths of time under 1 second here. Now, very short-term demands for current do exist when playing music, so in theory the capacitor can have some value. But it's highly debateable whether it makes an audible difference. I do know that lots and lots and lots of marketing money goes into selling capacitors, yet I've never seen a cap manufacturer invest in a real, controlled test that shows an audible difference when using their product. If someone knows of such a test, please link it.
Some people will promote capacitors as a way to reduce the strain on the alternator. I had a customer with an audio system under 1000 watts, and her alternator failed. I doubt the system had anything to do with the alternator's failure, but whatever. She had it replaced, and the shop that she bought it from refused to provide a warranty unless she added a capacitor to the system. That shows that even vehicle electrical system "experts" are muddled in their thinking about capacitors, because as you can see from what you've read above, a capacitor does nothing at all UNTIL the alternator is already overloaded! If the alternator can hold its normal voltage level, there's no current provided by the cap. It's only when the voltage drops, because of a high demand on the alternator, that the cap begins to do anything at all in the system.
