Agility and training for showing is totally different. They are for fun, and treats to teach dogs tricks and stuff is fine because it is not a required behaviour. I have no issues using treats to train my dog to jump over hurdles because it's not something I expect her to do all the time without hesitation. I will never use treats to teach my dog something as important as a sit stay or a required command. Also, if you use treats every now and then for training agility or fly ball, your dog doesn't come to expect treats all the time. They are still just used as an occasional reward, not for all the time training.
Training kids is different. When kids are young, bribery is sometimes the only thing that works, but when they're older, we expect more and we don't expect to have to bribe them to do what we tell them. Dogs only have the mental capacity of a 2 or 3 year old when they're full grown so bribery is harder to untrain, so why do it in the first place?
Treat training your pet to listen to you when you ask it to sit, is not a healthy, respectful relationship on your pet's part. This is all just my opinion and those who disagree are more than welcome too, but it won't change my stance on the subject.