the vast majority of Tuning Issues are to do with the 'nut' - especially if you 'know' how to properly wrap a string around a tuner post. Assuming you 'know' how to do that, the only advantage of 'locking' tuners is to make string changes quicker and easier. The reason you get 'tuning' instability is that the 'friction' between the nut and string is greater than the tension meaning it stops the string from returning to pitch. That could be because the nut slots aren't cut right or the material itself has more 'friction'. Even with 'straight' string pull, the angle of the slot on the 'back' edge of the nut down to the tuners can increase/decrease the 'friction', the width of the slot and string gauge affects the 'friction' etc and its that 'friction' that is the 'cause' of tuning instability. The Les Paul is an 'example' of this as the angle from nut to tuner, will create 'friction' that unless the nut is cut well, will lead to tuning instability.
Its often a LOT cheaper to replace the nut or at least check the slots or buy some 'nut lube' than buy a set of locking tuners.
I admit I much prefer Locking tuners myself but only because I dislike changing strings with all that wrapping and unwrapping around the posts - it really makes a difference to the ease and time taken. Therefore by choice, I'd go for locking tuners, but in terms of tuning stability, they only improve it if you don't know how to wrap a string round the post correctly and therefore can 'slip' or 'move'.
If your string looks like this around the post, you are asking for tuning issues...
Also Phil McKnight does test the Tuning Stability with the Trem doing dive bombs here - Skip to 13:30 to see the tuning stability test.