Big 3 on Stock Alternator Worth It?

BIG 3 just increases the amount of power that can flow through the alternator system. The alternator is not magically able to supply more power just cause the wire can handle it right? I doubt the factory wires are constricting their capacity. If you installed a high output alternator then it is obvious that you would want to use a higher gauge, but I would assume that the factory wires are sufficient for the amount of power the stock alternator is supplying? am I correct in this assumption or is my thinking flawed? also do amplifiers continuously draw all that power listen in the RMS rating, or is it always varying with the demands of the music and how loud you turn up your volume? so if I have my volume lower and my sub is barely hitting I would assume the amp is drawing less power than with the volume turned half way up and the sub going through full excursion? correct?

Amplifier demands are next to nothing when the volume is turned all the way down.  Most idle at less than 1 amp.  Some do draw 3 or 4 amps of current.

Factory wiring is the smallest possible size (and often not made using standard AWG size) that will support the needs of the vehicle, or the needs of the component it is powering.  Vehicle manufacturers do this to save weight and cost.  Adding ANY load to a factory system beyond that it is designed for can overload the factory wiring, so it is generally always a good idea to upgrade the Big 3 on any vehicle when adding electrical loads.

And yes, the power drawn by an amp increases as volume goes up.

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Ditto. IMO the BIG 3 never hurts. Whilst the big 3 does not increase alternator capability, it reduces the load resistance, hence more power from the alternator, and a higher voltage presented to the load(s). Conversely, imaging inserting a resistor in the ground or +12 paths....

YES!

the sub amp will draw current in bursts with the beat, if you are useing an amp on full range it will draw current more consistently.  and yes the louder you go, the more it draws.  A two amp system OFTEN uses as much current as the entire rest of the vehicle, so do the big three, its cheap insurance!