Clearly, you have never met this man or his family. That man is one of the best.
As for the tail set, to an outsider, comparing it to a harness is accurate. No, you are not going to hook one to the jog cart. It was for comparison purposes only. And really it kind of is a harness. You have a breast strap, a surcingle, a crupper. You have the main components of a harness, however the function is completely different.
Where I get my information is a lifetime of experience growing up in a competitive show barn, and by talking to and visiting and working in many different barns. I get my information from my personal experiences and from people who are more experienced than me. I do, in fact, know that with the sets come off with the show shoes in many many barns.
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The tailset video of his, as well as the others? Show that clearly.
And our horses wore their tailsets and show shoes, they were not pulled or removed during the winter, nor was any barn doing that that I know of.
Maybe in your experience it was? But not in mine.
Incidentally, what barn did you grow up in? Where at? What trainers did you work for, or did you show? What circuit did you follow? Who were the trainers you worked for?