I think one of the reasons there were few cats around is basically because they used to eat them. And once in a while the restaurant kitten catches would pick up an kitten they could find and take them back to the restaurant. I recall seeing felines in glass exhibits out leading of the restaurants. But somewhere within then and today they forbidden eating felines. So cats are actually not on the menu and today there are cats everywhere. Most of them started off in someone's house and acquired thrown away, because so many are incredibly friendly. Also they may have this thing about abdominal worms. And in those days China was not as modern as now so abdominal worms is a problem. Fleas aren't a really problem because they have tile surfaces and solid wood furniture.
Pet cats and mankind have been living in harmony for many years but that has not always been the truth. There were times when felines have been practically destroyed in the name of God. And what occurred the Black Death reigned supreme for a lot longer than it will. So we will go back to the beginnings of recorded record to the time of the pharaohs of Egypt. Here pet cats were revered as Gods and many were mummified to last for eternity. As the felines guarded the grain warehouses and killed the rats and mice that fed on the grain. Therefore minimizing famines, that were the curse of Egypt. It had been illegal to destroy cats in those times, like cows in India today.