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Coherent radio emission from pulsars originates from excited plasma waves in an ultra-relativistic and strongly magnetized electron-positron pair plasma streaming along the open magnetic field lines of the pulsar. Traditional coherent radio emission models have relied on instabilities in this pair plasma. Recently alternative models have been suggested. These models appeal to direct coupling of the external electromagnetic field to the superluminal O-mode ($lt_2$ mode) during the time-dependent pair cascade process at the polar gap. The objective of this work is to provide generic constraints on plasma models based on $lt_2$ mode using realistic pulsar parameters. We find that the very short timescale associated with pair cascades does not allow $lt_{2}$ mode to be excited at radio frequencies and the impulsive energy transfer can only increase the kinetic spread ("temperature") of the pair plasma particles. Moreover, under homogeneous plasma conditions, plasma waves on both branches of O-mode (i.e. superluminal $lt_2$ and subluminal $lt_1$) cannot escape the plasma. In the strongly magnetized pair plasma, only the extraordinary mode ($t$ mode) can escape freely. We show that any generic fictitious mechanisms does not result in the wave electric field of $t$ mode to have predominant orientation either parallel or perpendicular to the magnetic field plane as observed. Such fictitious mechanisms will inevitably lead to depolarization of signals and cannot account for the highly polarized single pulses observed in pulsars. We suggest coherent curvature radiation as a promising candidate for pulsar radio emission mechanism.