On a bit of a tangent...It sure would be a lot more work to create a wedge parallel to the post grain. And certainly seems like a more delicate joint. That video really demonstrates that it doesn't seem that the wedge is the weak point when oriented across the post grain. In the video, the "post" actually failed, which was surprising, as I expected the tenon relish to fail. What would be the reason to create a TF joint with the wedge parallel to the post?

In my opinion, the rationale regarding the wedge and trunnel system would be as follows:
The wedged through tenon is a joint which I have always recognized instinctively as exceptionally strong, and practical observation has only strengthened that assumption. While I don't think that the pegs are necessary to the joints function, I think that they would be added because... "why not". It's certainly not hurting anything and an extra 3 pegs or so per joint is not an unreasonable amount of additional work for such a critical joint, even before power tools. Plus I think it gives an additional structural fail safe. Would it not cross a builder's mind that wedges are not too difficult to knock out? If it was me building those New World Dutch barns I would peg those through tenons for no other reason than peace of mind. In my mind, timber framing derives a lot resiliency through well placed structural redundancy.