There is no such thing as purely positive training.
And sorry, but not only does my mentors experience disagree with you, but my own experience as well.
My experience is that there are things that are far faster and easier to teach with aversives or that some people are incapable of training without aversives, not that those things CAN'T be trained without aversives. I don't mean that as a dig, because there are plenty of things I don't have the time, patience, or ability to fiddle around with positively regardless of what type of dog I'm working with. Nor do I really care how someone else chooses to teach them. I don't even care if people don't teach them at all but choose to use management instead.
Having said that, I'm not going to say it CAN'T be done.