What's the point in a big ass alt if you have no decent battery to get topped up with any extra power you aren't using? Unless you're going to have your car running every time you play music, you'd be better off with batteries. And batteries can supply way more current than an alt can for shorter amount of times. You could pull 1,000 amps from a big battery for a few seconds with no problem, you can't do that with an alt though without putting heaps of strain on it.
Batteries supply current, as do alts. If you didn't have current, you wouldn't have power, you wouldn't have freaking electricity. Batteries just store their power in a chemical form, while alts convert movement into it.