In the parameter regime where the ion/electron–dust collisions dominate with respect to the plasma binary collisions, the presence of plasma fluxes to the dust surfaces and dust charge fluctuations can significantly modify the dusty plasma response to low-frequency perturbations, with respect to the multi-component response (no charging collisions, fixed dust charge). Here the response found from the kinetic theory which consistently takes into account collisions and charge fluctuations is examined, analytic expressions are given and the parameter regime where significant differences with respect to the multi-component approach arise is determined. The streaming instability is considered as a particular example and it is shown that both the real and imaginary parts of the frequency can be significantly changed with respect to the multi-component results.