I own guitars with and without locking tuners. From what I can tell they make very little difference in tuning stability.
From what I have read and watched they work by, clamping the string and only require a minimal turning, so they have less string to stretch out and the string can't slip out of the post. I personally don't see how having a big more string around a post is going to make any noticeable difference once the string has stretched out but, string slipping I have never come across before.
All of my guitars have trems and locking nuts apart from the locking tuner one which is fixed, so I have not really had to deal with strings slipping out of a tuning post, does this happen? Or is this mearly a problem made up by companies who make locking tuners?
(I do agree they make string changes faster, if anyone mentions it)
Tuning stability? Meh. Restringing time? I'll replace tuners on every guitar I keep for that sole reason.