In this paper we analyze by means of accurate Multi-Subband Monte Carlo simulations the mobility reduction associated to high-κ dielectrics in a large number of n-and p-MOSFETs. We argue that soft optical phonon scattering can not explain the experimental mobility reduction for neither the electron nor the hole inversion layer. In order to reproduce the experimental data, a large amount of Coulomb centers in the gate stack is required, which would result in a huge threshold voltage shift not observed in the experiments. Even if we assume the remote charge to be in the form of dipoles, the associated threshold voltage shift is still large and not consistent with the experimental findings.