After reading both the tau and pi manifestos I get the impression that it's quite an arbitrary choice: either the circumference is fundamental and angles are na

After reading both the tau and pi manifestos I get the impression that it's quite an arbitrary choice: either the circumference is fundamental and angles are natural (tau), or the radius is fundamental and areas are natural (pi). It boils down to a trade-off and you can cherry-pick examples where either is "more natural", but in a mathematical sense it doesn't matter a single bit and that's why we should not waste time on this, it doesn't bring anything new to the table.