Ah, if you've got the budget (and stature) of the U.S. Library of Congress, you can probably figure out how install all the necessary ductwork in a giant, multi-chambered old building that wasn't built with AC in mind. (Fun article is here about how they do it: https://www.aoc.gov/explore-capitol-campus/blog/librarys-hva...)
But it's worth browsing pictures of the abbey to get a sense of how challenging this would be. https://www.comece.eu/christian-artworks-benedictine-archabb... Most books reside in giant, wall-flush bookcases with no natural ventilation. Establishing decent airflow -- without accidentally ruining structural walls or turning the bookcases into perforated messes -- seems very hard.
Yes, they are just not popular here. All new US houses are built with airducts as well, so it's not just old homes.
By the way, I was always curious why installing splits _in_ the room. I understand multi-story apartments, where there's no other place. But if we're talking about detached houses you have an attic (where the airducts go), or a ceiling (where recessed lights go). Can we put splits in there? I can see problems with power delivery, condensate diversion, but they are the same if we install them _in_ the room. But in return you get fine-tuned climate control, and no pressure difference problems (no need for bypasses to prevent slamming doors with ducts).