The wedged through tenon is a strong joint but does weaken the post. This is the reason given in at least one source on the joint I have read why it is not used in softwood building work, anyway in these parts, and only found in oak frames, which it seems is not so on the USA side and also no longer adhered to in new buildings as I have seen it here too. What to make of it? I don't know, but at the same time am not one to readily disregard the old-time localized body up built-up knowledge in exchange for what I see as a muddled globalized confusion irrespecutful of conditions in the particular instance. (Ok, call me a timber frame nationalist, I admit it.)
I have to say I am skeptical of this "why not" rational for the wedge & pin combo. Usually variations in joint configuration are meant address particular aspects of placement, material and function along with habits, culture, environment. But take the wedge which is parallel with the post for example. One possible reason I gave earlier, another might be where the post, or lets say vertical member, because as Jay says it really is a joint more appropriate on a smaller scale, is small across grain and orienting the wedge in the length gives more bearing surface. I think the videos represent unrealistic situations and so we must disregard them outright. And back to my workbench but it could be any of the workbenches coming out of Scandinavia, where the vertical wedge makes perfect sense, in softwood by the way, when you consider the dimensions of the legs and stretcher configuration, the legs so narrow across the grain that wedging that way would be asking for trouble.