The integrated non-modal linear and renormalized nonlinear analysis of the temporal evolution of drift-type modes in plasma flows with a homogeneous velocity shear is developed. Analysis is performed in the time domain without spectral decomposition in time. It is proved that a long-standing belief that the enhanced decorrelation of the fluctuation by shear flow is the universal process in the turbulence quenching in shear flow is erroneous. In fact, the theory has a serious deficiency that renders it useless.