Even if it is carried out with no emotion, done with skill, etc - it is still a form of punishment. Correction is a form of punishment no matter how you try to sugarcoat it.
However not all forms of punishment are effective in correcting behavior. It must be immediately after the behavior and done consistently - the same rules as positive and negative reinforcement.
What effective training always comes down to is timing, consistency, the reinforcement/punishment fits the behavior, consistency, oh - and did I mention timing? I've seen people mess up all forms of reinforcement and punishments by being off on timing.
I think this is why inanimate objects will always be better trainers than humans. If you think in the case of an electric fence - most horses touch it once and know better, some need to try out other spots on the fence line, but they all learn immediately not to touch it
Or automatic waterers, it doesn't take long for a thristy horse to work out that pushing the little lever the water comes out.
The difference is the tools respond immediately to the stimulus, without thought or hesitation.
I find kids also make the best little horse trainers, I use Clicker Training at our rescue, it's fairly simple to get the gist of how to use it. All you need is good timing and an understanding that when the horse hears the "click" he's going to repeat whatever he was just doing to get more "clicks". So they need to be sure that they click at just the right time. The adults who come to learn (myself included when I first started learning about it), we get overburdened with the "hows" and "whys" we study the science and overthink every gesture and movement the horse is making. "well he backed up, but his head is really high, should I click? Ya I'll click" - well it's too late now! I find myself going through that scenario all too often. But the kids don't read into it! They just wait for the right behavior and mark it immediately! They each have their own pony project or two, some are big horses learning about riding, others are pony's doing unmounted agility and the kids have those ponies rocking! Us adults get so stuck on the science :P
This is a little video of one of the kids working with her pony, this pony came to our rescue feral and uncatchable. We left a short rope attached to be able to turn her in and out. This little girl got this pony following her around, learning obstacles, they do little jump courses and weaving cones (even with really crazy looking obstacles sometimes!). This video just shows her working on targeting work, working on trotting and backing up and spinning a little. Kids just give the response the horse needs, without overthinking it.