Key words...."number of reasons"
Tweeters will never be able to handle the power a subwoofer can. My home theatre sub only utilizes about 35watts @ 8ohms. Majority of mainstream subs are designed to handle a lot of power and are very inefficient. There's a number of reasons subs need more power these days...listening preference, design, marketing, spl, etc.
Bottom line is that those sub notes cause a spike in power needs. A poorly designed power supply in an amp will not pull consistantly on the alternator and battery. If his voltage is dropping we don't know why just yet. If he has a 125amp alternator I would be shocked if that's the issue. His amps are rated a little less than mine and all I have is decent entry level equipment. My guess is that the 8awg from the alt. can't deliver on those power spikes and the battery can't keep up either. In these instances a cap can be a band aid. You can try the big 3 as well but like Matt said...this is a science.
Think it through so you don't waste time and effort on nonsense and think LONG TERM DESIGN too.