Why does a black body emit at all frequencies at thermal equilibrium?
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It doesn't. When the average time to emit a single photon of some frequency is much larger than your observation interval (say, years, or if you go big, the age of the universe), it can be argued that this is the cut-off frequency. – Jens Nov 17 '19 at 14:36
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1A black body emits photons of all frequencies ($0$ to $\infty$), but only very few photons with energies greater than a few $kT$. See related question. – Thomas Fritsch Nov 17 '19 at 19:04