This is a common misconception about reward-based training, though. (Sometimes I see this disparaged by people less tactful than you as "I'd like to see you call a dog off a deer by waving a cookie in its face!!!") The thing is, that moment when you are in public and she is really excited and worked up is NOT a training moment. Training takes place before that - starting in low distraction environments and gradually building up to teach your dog how to stay focused on you in distracting environments. If your dog isn't so overwhelmed they won't take a treat, they aren't ready for the situation yet.
I think that's why this particular misunderstanding happens - it's a slow process to teach, increase distractions, and proof a behavior. In the meantime, you have to manage. And many people prefer things that work faster with less build-up.
Again, this is a misunderstanding. Just because my dog was trained and proofed with treats, it doesn't mean I must have a treat with me in order for him to comply. The first time I took Squash to an off-leash area, I was easily able to call him off wildlife - but he was a year and a half old. I didn't expect him to do that, and didn't put him in a situation where he might need to, until he'd already HAD the training. Waving a cookie under your dog's nose in that moment of fixation is NOT rewards-based training, it's bribery and distraction.
Mine... do? I'm not sure why you have this idea that dogs who were trained with treats will only respond if you are waving a treat in their face every time you ask them to do something?
I don't HAVE to, either, and usually I don't. But sometimes I do, because there are numerous opportunities to train and proof new and old behaviors every time I am interacting with my dog.
