In spite of lots of attempts, polymer dynamics under fast flow still remains unrevealed. One of the unsolved issues is the insensitivity of end-to-end relaxation of entangled polymers to shear reported by Watanabe et al. [Macromolecules 35, 8802 (2002)] and recently re-examined by Horio et al. [Macromolecules 47, 246 (2014)]. In this study, the effects of degree of freedom below entanglement segment were investigated on the polymer dynamics by the modified multi-chain slip-spring model. The model was validated through the consistency with earlier simulations and experiments for the shear rate dependence of viscosity, end-to-end dimension projected in the shear gradient direction, entanglement density, and anisotropic diffusion tensor. However, the end-to-end relaxation is accelerated under fast shear to follow the earlier multi-chain slip-link model and modified tube model simulations. The results are insensitive to the number of beads between entanglements, supporting the validity of further coarse-grained models. Nevertheless, the flow insensitivity of end-to-end relaxation of entangled linear chains has remained unsolved.