Thank you! Some of that looks quite complex. But perhaps I can translate some of these concepts to 2D, which looks easier for prototyping.
I had a similar idea this morning. Thank you for backing it up with a real life observation! The algorithm that I use to design the tree structure makes it straight forward to get this – in your words – cumulative cross sectional area. For an example, see my post in the thread: Fast way to pipe polylines? (with varying radius)
Regarding the issue that I raise in our thread here, I wonder how it would look if the length of each branch is defined by the cumulative cross sectional area. Thicker branches can be longer. Kangaroo could be used to find a solution.