>> we filled our red plastic cups to the brim with Bud or Miller Lite or Icehouse...
I would say that if that's the caliber of beer you're drinking - which makes up a significant portion of most people's college beer - then screw the head, and just fill that red cup up all the way. No one drinks Icehouse or Bud for the flavor; they drink it to get drunk. You could pour some Bud perfectly into a freshly cleaned glass, and it would still taste bad.
Once you've moved on to better-quality beer, then yes - bring on the head.