I'm from the recurve world but have heard loads about freestyle shooting.
I know of two advantages for shooting with 3 under (only one for instinctive)
Having a 3-under allows for string walking. What this is, is basically the ability to pull the string at a different position hence changing the distance of your shot. The archer would then be able to maintain his sightpoint (or if instinctive, your feel/instinct) despite the change in distance of the target.
With a 3-under, it allows you to sight down the arrow much more easily as the arrow will be much closer to your eye. (not applicable for instinctive).
You will not see string walking in recurve as we have sights wherein we will be able to calibrate our sights to the distance that we're shooting.
Adding a better description for string walking as I've noted my description above is abysmally poor :)
String walking is basically changing the distance between your hand and the nocking point of the arrow.