Equivalent "capacitative reactance" for calculating rms current under mixed-frequency AC voltage waveform
My initial reaction is that Xc(ω) is additive across the frequencies


Take the case of a simple capacitor of 1uF at 1kHz - it has a reactance of 159 ohms. It's as simple as that. 

Yes it has a reactance of 15.9 ohms at 10 kHz but nobody goes on to say that the reactance is 159 ohms in parallel (or series) with 15.9 ohms. To do so is to miss the whole point.