Why does adding a battery or replacing the existing one upfront with a larger one stop peoples lights from dimming though?
It never has, hence why you always see people posting threads like, "why are my lights flickering, I have 1-2-3 batteries, etc.."
The lights will stop flickering because their amps draw so much power that the alternator is no longer keeping up at all, the voltage drops to the battery's voltage at that point the battery is supplying a steady stream of the power to the system, lights stop flickering, lights are dim but not flickering, but if you read the voltage you will be looking at a low voltage of 12.6 or less. This would be a voltage drop. this is what we are trying to prevent. It would be akin to just disconnecting the alt, or turning the car off.
Simplified,
When the lights are flickering, its because your alternator is bouncing between its normal 14v+ charging voltage and the battery's 12.6 resting voltage. trying to keep up.
Once the alternator is way out of its league, then the lights stop flickering and you will just have a low voltage situation. Adding another battery only makes the alternator have to put its current into an additional device compounding the problem.
A low voltage situation is hell for the alternators rectifier diodes, and its voltage regulator. because more current is constantly flowing through them. this heats them up, and eventually kills the alternator.
make sense?