Transformer section and magnetic field
A larger section increases the core's permeance, and thus the inductance of the coil on the core.
It is not visible in your first formula, because this relation apears only in the second formula - the permeability. This quantity depends on the permeance, and thus on the core section.

Whatever the section of the core, the flux density will always be the same...

Nope, because the permeability in Eq. 2 will change when the section changes.