The displacement current is introduced so very early in Maxwell's book
that its later inclusion to ensure a divergenceless magnetic field appears
to be natural.
Perhaps the point is that whenever we change the charge inside a
volume, the flux of the electric field through the surface of the volume
also changes. Since no one has ever seen an electric charge, (Current
size limit is less than 10^-17 cm.) the only way we have of detecting
charge is via Gauss's law. Which comes first, the field or the charge?