To pitch in, I've noticed silk of common variety, and more often the rare variety, to be extremely hard to find on other civilizations. Often I see plant fibre - but that is it, no wool, no silk, no rare silk, etc traded by any civ I've met in my last 5 forts (nor can be taken from embark).
My caverns generate just fine, so I'm perplexed what the issue is myself. Just confirming I've seen this issue too (on the lack of silk) - rather frustrating when you got a strange mood. Shrines are great!... if they work. I've had to run 30+ dwarves on silk to get 1 piece after 5 minutes before, hahaha.
Does anyone here know how civs 'gather silk and rare silk'? What they require? That might help isolate the OP's problem, as I got a few ideas (that aren't just dry/non-genning caverns).