I've read many times that a zero fret improves tuning stability. It seems like a good idea to cut grooves in the nut so the strings have as little contact as possible, similar to a zero fret.If I could expand on this, a perfect nut will either let the string move without any friction, or it won't let it move at all. Anywhere in between is bad.
My way of doing it where I lock the string at the tuner and use a zero fret for essentially no friction at the nut is almost as stable as a locking nut, but without the drawbacks.