One technical point about resonance: the fourth-power law only applies when the driving frequency (i.e., the frequency of visible light) is far below the resonant frequency (which is in the UV region of the spectrum). The approximation breaks down the closer you get to the resonant frequency and also above.

I was confused about how a monotonic function (f^4) could possibly describe a resonance phenomenon (which ought to have a strong local extremum), and this is the answer.