I’m not a fan of AuthaGraph at all. It has horrible distortion look at Brazil or Alaska - and it’s proprietary (creator never released the actual map details, so you can’t make your own...) The worst thing, in my eyes, is that the distortion is unpredictable. Looking at a map where Canada is too big, you can mentally imagine Canada as smaller. But you can’t mentally undo the multi-direction transformation of Alaska into not-Alaska. The distortion is so bad that real world things like a road trip through South America would end up looking completely different from this map to another. You better hope you never get on a boat or a plane using this map - try tracing a straight line if you want a laugh. (The unfortunate distortion-hacking done by its creator effectively dumped the distortion in the oceans, so good luck if you ever go there.)

Design features like “you can do nifty origami with it” shouldn’t factor into if a map is used or not.

In my opinion, if you want something modern and cool, and you really care about pure accuracy, go with Waterman Butterfly. If you want something four sided and traditional, and relative sizes are slightly less important (but still important), go with Peirce Quincuncial - which, I might add, has far better looking Tissot’s indicatrices.