dbx engineers actually wrote a white paper on de-essing that was an AES show preprint several decades ago. Indeed there are different strategies for frequency selective dynamic processing. While you don't want one section of the frequency spectrum to cross modulate another, one ASSumption often made about de-essing is that when it is used, the HF signal is the dominant signal at that time, so there is no or little benefit from band splitting.
An Additional benefit of keeping the gain element wide band is that you can layer multiple dynamic effects on top of each other by summing the sundry control voltages into a common VCA. Over the decades I have done a few commercial designs with de-essers combined with comp/limiter/noise gate. etc.
A multi-band dynamics processor is another animal entirely useful for more than de-essing which is a pretty narrow specific application.
Of course opinions vary...
JR