If I am correct, the reason for string trees on certain guitars are because the strings must be at a certain angle (the break angle) to the nut/saddle. Does anyone know what this exact angle is? And what happens if this angle is not met?
The reason is actually to minimise the chance of the string popping out of the nut, and on some guitars to increase friction at the nut.
I have only had a guitar without a string tree cause problems once - it was a very cheap thing I had about 25 years ago, and when playing energetic rasgueado I could pop the D string out of it's notch on the nut.
Never had a problem since, and only two of my fixed bridge guitars have string trees.
Amusingly, one of my guitars with a tremolo and a locking nut also has a string tree - not sure exactly why...