Intuitive Question - effect of capacitor on this common-source stage
If you ignore non-linear effects, i.e., small signal, Vout neither falls nor rises, it stays the same. 

The problem lies in that we are speaking about different things. The DC value of Vout (which is the equation you wrote) does not change. 

However the small-signal (AC) magnitude of Vout goes down as you increase the frequency. More and more of the AC current goes through the capacitor and less and less of the AC current goes through the resistor. 

But this AC signal is riding on the DC operating point. And that does not change. 



Nonetheless, if you consider non-linear effects, there will be a change on the DC operating point due to distortion of the AC signal. Consider the components introduced by a quadratic distortion of a sinusoid. This will produce both a second harmonic and a DC component that changes with frequency and input magnitude.