Valid question Cancers. In a typical drums, bass, guitar, vocals mix I can see why someone would scratch their head if someone asked this question
Not sure if that's the mindset you're coming from or not, but if you are, I totally get the WTF? reaction
But for someone like me who does things such as use a trombone sample as the carrier in a ring-modulator to mangle a perfectly good piano part, or who doesn't use Melodyne (or rather in my case Cubase's VariAudio) as a pitch correction tool but to completely reshape a melody, a side-chainable multiband compressor is just a natural progression.
Don't think "problem solving". Think "sound manipulation".
In this case I would key a band (or two) off of a track that likely wouldn't even be sent to the main outputs, would be silent, and only be used to key the sidechain. Something like this, for example a drum loop, would be used to rhythmically duck a certain band of frequencies of a part, say a synth pad for example, to add timbral interest to it. Think of turning the gain knob on an EQ band in rhythm to another part. Just another way of filtering, yet different from your typical filter sweeps.
Although, I can also think of at least one "problem solving" instance too, but I don't want to cloud the topic at hand, which is...
Is there a side-chainable Multiband Compressor?