A thought:
Caroso's two books show a strong (and increasing) personal preference for symmetry. He likes figures done on the left side to be repeated on the right. If one person does something, the other should do it too, for balance. He prefers even numbers of repeats (so you can do something the same number of times on the left and the right).
Yet a goodly number of dances, especially in Il Ballarino, are rather asymmetric: patterns of steps done only once, or three times, figures done turning left, but not echoed on the right, the man and woman doing different figures.
Many of those dances are good choreographies: charming, sometimes quirky, often feeling more balanced in performance than they seem on paper. The cascarda Bella Gioiosa is an example - it looked to me arbitrary and rather unbalanced on paper, but in practice it's a delightful dance, and very popular (more so than some that are more regular). Recently, I've noticed the same with the mutanze in Caroso's Passo e Mezo: they often appear at first glance to be a somewhat arbitrary sequence of steps, without internal repeats to give balance and structure; yet when danced with a partner who is doing Caroso's passegio they are full of seemingly-spontaneous moments of graceful interaction.
On the other hand, while some of Caroso's strictly-balanced, strictly-symmetrical, tightly-structured dances are lovely, others are rather dull: formulaic, pleasantly-figured but lacking charm.
My thought: that's not coincidence. Caroso's strong aesthetic preference for symmetry meant he had a much higher bar for dances and figures that didn't suit his ideas about good choreography. A perfectly-balanced balletto, with verse and chorus, all figures repeated on both sides: that suited him well, so might make the cut without being otherwise spectacular. Asymmetric, unbalanced, full of things that tweaked Caroso's strong preference: that had to be really good to make into his published works.
Maybe that's why so many dances it seems Caroso ought to have disapproved, but that nevertheless made it into his books, are so satisfying. They don't look good on paper but they feel good to dance, sometimes for reasons that are hard to pinpoint. Maybe Caroso felt that too, and kept for us the best ones.
This is a part-formed idea based on my gut-reactions to the specific dances I'm most familiar with. The test: a more systematic check of the rest of the corpus, to see if his asymmetric dances are consistently good (or at least: consistently appeal to me); and the sense of dullness I associate with his more symmetric dances is similarly pervasive. Also: a check of other sources to confirm my impression that the less-symmetric dances are more likely to appear in multiple sources, and so presumably were more widespread.
Finally, to investigate the difference between the statements "Caroso had a stronger preference for symmetry than most (contemporary and modern) people" and "Caroso's asymmetric dances are therefore unusually good in other ways": see if the pattern holds for other authors who display less of a preference for symmetry. If it does - maybe I just like symmetry less than Caroso did. If it doesn't - if the symmetric and asymmetric dances feel similarly-good to me, in anthologies collected by people who showed a less-strong preference for symmetry than Caroso's - then that supports the idea that his dislike of asymmetry caused him to keep only asymmetric dances that are otherwise really good.