I have 2 former BL horses in my barn right now....a 5 yo, and a 15 yo. I see no damage , physically or mentally. They are both ridden barefoot now. Neither of them have any mental problem with farriers, or having shoes nailed on.
The racking horse show in the video is not the same as a TWH show with flat shod classes. The flat shod classes I saw WERE western pleasure... and I don't watch AQHA, APHA, AHA WP either, unless I know someone showing. But they probably think dressage is boring, and I am not critical of that, to each his own.
I would love to watch the Versatility show! That looks like fun to watch.