The difference is not exponential, if I may nitpick. It is sublinear in the case of the "triangles example" - WCO would produce O(n^(1.5)), binary join will produce O(n^2), the difference is O(n^(0.5)) or O(sqrt(n)). The difference is big, but not exponential.

Good nitpick, I think you can construct larger rings where the difference becomes larger than one, but I might be wrong. The dynamic variable ordering trick makes a huge difference in practice, especially when skew is in play. (https://arxiv.org/pdf/1310.3314.pdf)

In general you're right, WCO joins are a relatively young field of study and sometimes struggle with large constant factors, but they are maturing quickly and in a limited (triple) setting like the one OP "wished for", a lot more feasible than for the general case.

Thanks for the interesting discussions, looking forward to reading the references you provided in depth!

Edit: I just remembered this paper, which might be of interest to you. They seem to recover WCO bounds in a pairwise setting, by choosing very smart intermediary join representations: http://www.cs.ox.ac.uk/dan.olteanu/papers/co-tr16.pdf

My old idea was to perform planning after some of the work has been done, because remaining statistics can be different. These papers are of great help!