I've been wondering this recently. My intuition says that a voltage drop across a dependent source is no different than any other circuit element whose response depends on the inputs of one of the independent sources. But I don't feel like that reasoning is rigorous enough. How exactly would this principle regarding treatment of dependent sources be derived?
Answer
Two ways to think about this:
If you disabled dependent sources when modeling the contribution of a dependent source to the circuit, they'd have no effect on the circuit. If you did another round of superposition to get the contribution from the dependent source, there'd be no output because there wouldn't be any independent source present to drive the dependent source's input. So you might as well have never put them in your circuit model to begin with. Which obviously defeats whatever purpose you had in including the dependent source in your model.
Dependent sources are no different from other elements in that they respond to stimulus from the independent sources. For example, you could model a resistor as a CCVS whose input and output ports happen to be connected in series. So any argument you have for removing dependent sources during superposition solutions also applies to resistors, capacitors, and inductors. And if you removed those from your circuit, you'd have no circuit left. So obviously that's not what you should do.
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