Although the intelligent reflecting surface (IRS) has attracted significant interest, existing works have not addressed adequately the impact of its inevitable phase errors by taking into account their randomness. In this work, we focus on covering this gap by considering a general large IRS-assisted multi-user (MU) multiple-input single-output (MISO) system with imperfect CSI and correlated Rayleigh fading. On this ground, we perform a beneficial channel estimation (CE), and we obtain the achievable sum spectral efficiency (SE) in closed-form in terms of the large-scale channel statistics. The whole approach suggests a novel computationally efficient method for reflect beamforming matrix (RBM) optimization of IRS-assisted large multi-antenna systems that can take place at every several coherence intervals. Monte-Carlo simulations verify the analytical insightful results. Among the observations, we highlight that if the IRS phase noise follows the uniform distribution or if independent Rayleigh fading is assumed, the use of the IRS has no benefit.