I use both, and a lot of ADS folk use a good strong "W-AA-LK" or "T-ROT!" to get their horses going somewhere. Of course, they're coming from the perspective of people who would be handling a large team and you ain't gonna expect four horses to go perfectly with each other for just some chicken-kissing!
Seriously, it is fine.
I'm not sure how much more "nervous" a horse might get from not having verbals, I mean Kody knows perfectly well what a double cluck or a kiss means, but I trained him for those to be interchangeable with the verbal cues. Those horses you saw are probably nervous because of the overall feeling of their training, i.e. high pressure and focused on turning it on in the showring.
As for them knowing what to do to the point of doing it themselves, I'm afraid I would be a bit alarmed if my horse is responding to the overhead announcements and not me! I know old show horses get that way, but to my way of thinking that's a bad thing. They should ALWAYS be paying attention to the one in the driver's seat and not to anyone else. The voice is a substitute for the LEGS, not the REINS, and I don't want my horse downshifting without any need for those reins. No, I shouldn't have to haul him back to get him to slow down or transition. But those reins are the means by which I tell him
where and
how fast I want him to downshift, something that is very important in obstacle or dressage. I use the voice cues, but I half-halt with the reins first to warn them and then add the voice on top of and just after the gentle rein cues. It's more a reinforcement and clarification of my request than functioning as the command itself.
Example of why this might be important: what if your harness broke and you brought your horse back to a walk, but the announcer asks for an extended trot at that moment (not seeing the problem yet) and your horse does it?? Your horse needs to do what YOU want it to and not worry about anyone else. Your reins are the only thing your competitors can't interfer with.
Use them!
Sorry to have gone on here.
Leia