Could the acute disparity in numbers between Volantene Freeborn & Slaves represent the lingering demographic impact of disastrous losses during the Tiger Wars, exacerbated by the “Blood Purity” taboo? (which ensures that Freeholder women who look beyond their own city or class for spouses are held to be polluting themselves and thereby diminishing the numbers of Freeholders still further, rather than helping to regenerate their class).

It could…except we see pretty much the same ratio in all of the Free Cities that have slavery, as well as the cities of Slaver’s Bay, etc. Also, at no point when Tyrion or Quentyn are in Volantis or when Aegon is being quizzed on Volantis does anyone mention that.  

“So the political-economy mystery here is what would have caused such a sharp increase in demand to meet the increase in supply.” The need for Unsullied and other slave soldiers?

Plausible, except that we don’t see Unsullied used in large numbers inside the Free Cities other than in Qohor. And we need to explain not just where Astapor is offloading its “supply,” but also Yunkai and Meereen.