This explains it well...
http://www.easyperformance.com/Alt_R...wire_Desc.html

This is my personall opinion; no matter what you run from the battery which is in the front, to you amp in the back, of it pulls enough, lights will dimm. The reason is the fact that the alternotor has a "turn-around time" if you will. When the bass hits, it draws a substantial amount of power, but not long enough for the alt. to pick up the lag. That is why a cap is not so much a bandaid but a float device for the system. You keep it as close to the amp as you can so when pulsed-power is pulled, it pulls from the cap.

isin't that bad for your battery to have an alt that powerful when all your accessories are off?

No.

The reason behind this answer is that when the accessories are off and the battery is fully charged, the system is designed to not overcharge and not deliver power when not needed.

Alts have voltage regulators in them.