None, really it is just a different construction method. See below.
See below.
With a none locking tremolo system, the point is to reduce all points of friction as much as possible. Effectively, anywhere that a string could not return to the same place after tremolo use will change its pitch. This is factual due to physics.
See below.
Indeed, the point also requires the elimination of string trees, as they introduce additional points of friction and changes of angle to the strings. If a string tree is used, it would have to be well lubricated.
A very well-cut nut and set up guitar is needed also. If the nut is not correct, it can also produce friction, or cause citar like sounds, and various other non desired elements such as the break point of the string not being at the leading edge and throwing intonation out.
All string trees do is put an additional break angle on the string, equivalent or similar to what a tilt back headstock gives. This can hide the effects of a badly cut nut and is a large part of why factories use them. But they do nothing to help the tuning stability with a none locking system.