Using the non-equilibrium molecular dynamics (NEMD) simulations and the time-dependent Ginzburg–Landau (TDGL) theory for solidification kinetics, we study the crystal-melt interface (CMI) kinetic coefficients for both the soft-sphere (SS) BCC-melt and the FCC-melt interfaces, modeled with the inverse-power repulsive potential ((Formula presented.)). The collective dynamics of the interfacial liquids at four equilibrium CMIs are calculated and employed to eliminate the discrepancy between the predictions of the kinetic coefficient using the NEMD simulations and the TDGL solidification theory. The speedup of the two modes of the interfacial liquid collective dynamics (at wavenumbers equal to the principal and the secondary reciprocal lattice vector of the grown crystal) at the equilibrium FCC CMI is observed. The calculated local collective dynamics of the SS BCC CMIs are compared with the previously reported data for the BCC Fe CMIs, validating a hypothesis proposed recently that the density relaxation times of the interfacial liquids at the CMIs are anisotropic and material dependent. With the insights provided by the improved application of the TDGL solidification theory, an attempt has been made to interpret the variation physics of the crystal-structure dependence of the solidification kinetic coefficient.