Common as in that specific system, not really I don't think. Useful, I suppose. I've seen and done similar things, but not with a clicker. You can just say yes/no, etc. It's helpful for them to get immediate feedback while they continue and figure out how to make the changes without being positioned, although I think it works better with older girls. The problem is if they don't fully understand, they'll just keep on going...you have to be sure that both partners really understand what you want, otherwise it can just confuse them more. We used to do routines and the coach would tally it and once every lock that was "hit" earned a piece of candy. That was because she had a bag of candy left over from Halloween, usually it just got tallied and a yes or no. Poor lock positions are one of my pet peeves too.
I think "random" reinforcement is just as useful though once they get the idea but just have to work hard to always do it. We used to have to do so many of something right and if the coach saw one wrong, start over, or make 5 in a row, show the 6th, if you don't make it, start again. Or do a routine, if you miss so many lock positions, do 10 rows of step lock, etc. That can be demoralizing if you're not careful but sometimes they just really have to always do it and not just do it when it's the "focus" that time. So I think it's helpful for them to get the idea of doing it consistently, but once they can do it, I prefer to have them go about a sequence and reinforce the problem areas from a more random standpoint than just repeating the same skill. They seem to get more out of that - but that's just my experience. Initially in trying to correct a problem or weakness, I do find repetition very helpful though. Sometimes they're just not aware of how the "right" feels vs the "wrong."
I tend to agree. Those clickers are normally used for training dogs. While I actually believe kids can be trained similarly to dogs (i.e., positive reinforcement works best), I'd be reluctant to use a method that made them feel like dogs.
I don't really think it's degrading. I don't see kids associating it with being treated like a dog, unless they were told to associate it that way, which would be weird. I think most of the kids I work with would think it was "cool!" They like to be "in charge", do new things, use new stuff, etc. Kids LOVE those little clicking counter machines (click it and and number goes up). Even 8-12 year olds to some extent (by the teen years it better be digital ) And I think giving them an opportunity to participate and teaching them to pay attention and recognize things in others is important. But like so much it is a battle for time and payoff...sometimes it's faster for me to just correct it than to enforce not only whether each person going is doing it correctly, but that each person watching is watching correctly. But it is a way in some cases to cut down on talking or wandering while waiting to go and having an active job while waiting. So these systems (any sound cue or partner feedback such as everyone scatter around the floor - person doing routine has to make effort to make eye contact with each person, etc) has it's time and place but I haven't ever used it or seen it used as a primary method of reinforcement. That's not to say it wouldn't work, I just don't know anyone who uses it as their primary method.
I am a former special needs and early childhood teacher and now am a speech pathologist. While I am sure this technique works, I would never use it, especially for gymnastics. It seems way too distracting, waiting for that click to happen. I have to imagine it takes away concentration and for gymnasts on the beam or on bars... just seems too risky in terms of potential injury due to distraction. As for other situations (they showed tying shoes, writing), I just think there are more effective ways for immediate feedback. Definitely not a fan of this...
As a gymnast, I would find this very annoying and frustrating in practice. It might work for some gymnasts, but for me I think that the click is very annoying, and instead of focusing on the click you instead almost focus to hear the click. If you don't get the click, you don't know what you did wrong, and sometimes that's harder to figure out. The last thing, is that I would get VERY frustrated. I think that with positive feedback would be nicer, you know you did something right instead of some click. It kind of takes the joy out, when you work so hard to do something right it's the best feeling to finally be told by a coach that you did something right.