Well, they do help in tuning stability. See, if the downward force of the strings on your nut (*I'm starting again*) isn't enough, there'd usually not be enough tension to keep the string from warbling (changing pitch) when you pluck it hard. You'll notice that a G string (*cracks up*) for example seems to have a little less tension without a string tree than with. Whether it's perceived or not, I'm not sure, but in my own experience, it seems so..
I'd better stop before I make any more crappy, oblique innuendos..