I'd be curious to know specifically what amp and subs you're dealing with.
I'm sure you're going on the assumption that you've taken all the stress off the alt and placed it on the caps. That's not at all the case.
The alt IS the source. It's the component in the system with the highest potential voltage. Adding all the batteries and/or capacitors you can fit in the system won't change that.
You've loaded the alt down to the point where it's fighting a losing battle.
Without the caps - when the amp's demand is high the alt is maxed out, and the car's voltage quickly sags to battery voltage. When the amp's demand is low, the alt actually has a chance to recover, voltage spikes back up to 14v or so, seen in a brightening of the lights.
now - with all the capacitors to charge -- once the bass hits, the alt maxes out, just like without them. Voltage sags somewhat slower to batt voltage as the caps discharge. With 40F it might take a few cycles to get to 12-12.5v, but it will get there.
When the bass note stops, the alt begins attempting to charge the caps and the battery, but eventually it comes up short. Voltage doesn't recover to 14v. Next bass note, alt is already maxed out, voltage is already at or near battery voltage -- you see no dimming.
So what you think is a problem solved is actually just a problem covered up, but now slightly worse since the high points of voltage aren't as high as they were before, and the low points are steadily getting lower.
The fact remains, the alt is being severely stressed. The case is probably too hot to touch, while the system's playing, and every minute you play the system at high volume is one minute closer to a failed alt.
Good luck with that.