Bullet points -

1 The transverse arch of the foot contributes more to arch stiffness than the longitudinal arches (see PDF below )

2 If the transverse arch did not extended into the forefoot then ,since systems tend to fail at their weakest point , the forces acting on the foot during gait would tend to flex ,distort and perhaps fracture the metatarsals .

3 The metatarsal parabola gives rise to ,or makes more pronounced ,the distal transverse arch during gait ,in the manner laid out in post #1 .

4 The tensioned transverse ligament /metatarsal/tarsal arch component of the system means that the metatarsals are subject to compressive and stretching forces during gait and not flexion which they are less able to tolerate .This is explained in post #5

5 One of the roles of the intrinsic foot muscles is to help regulate the transverse and longitudinal arches to ensure a proper distribution of forces throughout the foot .They must be strong enough to do this or foot pathologies are likely to develop .

PDF curvature of the transverse arch governs stiffness of the human foot

https://www.eiseverywhere.com/retrieveupload.php?...



The stiffness of shallow thin shells has two asymptotic regimes, one that ... A. The human foot has two distinct arches in the longitudinal and transverse directions ..