IMO there really is no benefit to locking tuners on a non-trem guitar except for (sometimes) making string changing a few seconds quicker. All the real benefit is on non-locking trem-equipped guitars.

If the tuners are made well, then they won't break strings. I've had both locking and non-locking tuners with sharp edges to the post holes that broke strings until I sanded the sharp edges off. After that they were fine.

The extra string turns on non-locking tuners do take some tension off the string where it goes through the post hole, but as long as the edges of the hole are smooth, there really isn't an issue. A few minutes work with a round needle file and some fine grit sandpaper and you should be able to cure even the roughest edges on a set of tuners. It's certainly worth smoothing over the edges of the locking pin with some sandpaper as they can also be a bit rough.

I haven't noticed any difference between locking and non-locking tuners on tone. Locking tuners will generally be heavier than non-locking, so you generally aren't comparing like-for-like, as extra mass at the headstock is something that (in theory) can also alter the tone of the guitar. But I really can't see how a few extra turns of string changes the tone. You've got the same string tension pulling in the post with both types.

One thing that can affect the tone (slightly) is the string break angle. On non-locking tuners, with a typical 3-turn wrap, the string is lower down the post where it leaves the tuner than on a locking tuner with the post hole at the same height, so its break-angle will be a bit greater. So with locking tuners, you want to be careful that you don't buy a set where the post hole is too high up the shaft. Worth looking at the dimension drawings. Height adjustable post tuners, or selecting individual tuners from a staggered height collection are an option if your headstock hasn't already got a decent break angle itself (e.g most Fender styles) and the top of the headstock isn't that far below the top of the nut.

All the time you've got a near constant tension on the string, a non-locking tuner will hold the string in place just as well as a locking tuner. It's only when you add in a trem and you take a lot, if not all, the tension off the string that the lack of multiple turns on a locking tuner is of benefit.

With a standard tuner, the multiple turns around the tuner become loose, the string shrinks slightly as the tension is reduced (just think of the string as a spring) and the wraps lose their previous position. When the trem is released and the strings come back to pitch, then the wraps can end up in a slightly different relative position and the strings then go out of tune.

With a locking tuner, you should only have 1/2 to 3/4 of a turn at most around the post, so you've no string against string friction to worry about, so the string goes back to the previous tension and (hopefully) stays in tune. But a badly cut nut is still the main point of most tuning issues.