On short length and time scales, the collective kinetics of relaxation or structure formation in multicomponent polymer melts, such as homopolymer blends and copolymers, is influenced by the subdiffusive single-chain dynamics. We compare the predictions of the dynamic random-phase approximation (D-RPA) and dynamic self-consistent field theory (D-SCFT) to that of particle-based simulation, focusing on the decay of a density fluctuation in the disordered phase, the spinodal phase separation after a quench from the disordered phase, and the response of the disordered phase to an external field. D-SCFT with a wavevector-dependent Onsager coefficient qualitatively fails to predict the time evolution on time scales shorter than the Rouse relaxation time of the underlying polymers, whereas D-RPA successfully captures the collective behavior observed in particle-based simulation. Extensions of D-SCFT, employing a time-dependent Onsager coefficient that is derived from D-RPA and that accounts for the subdiffusive single-chain dynamics on short time scales, are discussed.