Watching this video I'm left wondering why exactly a hardtail guitar would need a locking nut? This is something I would typically associate with a floating bridge? Does really low tuning give a guitar tuning problems?
It's because his signature model uses a blocked Floyd Rose trem, basically. He keeps the locking nut and bridge fine tuners like a FR guitar would have, but the bridge itself doesn't move. This is probably because he has always used locking trem systems, and it's more personal preference. He doesn't technically need the locking nut and could tune at the headstock pegs, but he uses a locking nut and the bridge thumbscrews to tune like a FR would.
It's a 'hardtail' based on a blocked off FR trem system. He still uses a locking nut and bridge thumbscrew fine tuners like a FR. It's just a personal preference/signature model design quirk. There isn't a practical reason to do this - he wanted a FR designed bridge and tuning system without the floating/trem aspect.
Having the part of the string which could move trapped with a clamp, it obviates any movement that's likely to happen - and that would be behind the nut, particularly round the posts, which after all should be wound properly - e.g. tight and secure. Possibly a case of belt and braces - and a piece of string, just in case! Must make re-tuning a pain when it does go out, although (theoretcally) it never should...
If you bend strings a lot, or hit them with aggressive strumming you can pull them out of tune on the post quite easily by disturbing the string wrappings, especially if they are coiled untidily. Comment : Doesnt that video show a floating bridge though ?
Locking nuts are solid chunks of metal which affects the tone of the open strings; possibly the player likes how the open strings sound with a locking nut. It's easy to adjust the string action at the first fret with a locking nut: the locking nut comes off with simple screws that go through the neck (no glue), and a shim can be inserted between it and the neck easily (such as a strip of wood veneer, or aluminum from a can). Locking nuts last decades without significant wear and don't require slot filing maintenance. (I have a nearly 30-year-old locking nut that required no maintenance other than one replacement of the three clamp screws.) Since the strings don't move, locking nuts don't require lubrication to remove unwanted string sticking. If a quality string is used with good tuning stability, it never needs to be unlocked over its entire lifetime; the bridge fine tuner is all that is needed, at most.
Here is something to consider. With a locking nut, it's possible to remove the bridge without unlocking the strings on either end or detuning them. You then have access to the fretboard and body for cleaning or other maintenance or alteration such as, oh, swapping your pickups. Then everything can be reassembled, and the guitar will come up in tune!
You can even take the locking nut off without unlocking the strings, and change the shims to alter the nut action. (The guitar won't quite come up in tune then, but close.)
Now let's talk about other practical reasons for going with the locking nut:
The locking nut likely came with the bridge as part of a set. People don't like to break up sets. What are you going to do; throw away a perfectly good nut because it's strictly not needed, and purchase a different one? Also, the locking nut and bridge have a matching appearance if they are from a set, like the same finish (both are black, both are gold, ...).
the hard-tailing could be reversible, too. If the guitar is converted to floating, the locking nut will become important.
a locking nut will still function as a nut if the locking blocks and screws are not actually installed to clamp down the strings. Why not just go with that nut?
the neck is probably pre-drilled for a locking nut, making it an easy install, and the spot where the nut goes is more or less correctly recessed.
the headstock of the guitar may be of such a design that the strings branch into an aggressive fan pattern after the nut. That generates sideways pull on a nut that a locking nut can handle, even without a "string tree" device present. If you examine any traditional guitar with an ordinary nut made of bone or whatever, you will not find any crazy string angles between the nut and tuners. The strings either go straight to the tuner winding posts, or at gentle angles.