I believe one of the reason why there were not many cats around is basically because they used to consume them. And every now and then the restaurant cat catches would pick up an feline they could find and take them back to the restaurant. I recall seeing felines in glass displays out the front of the restaurants. But somewhere within then and today they suspended eating pet cats. So cats are now not on the menu and today there are cats everywhere. Most of them started off in someone's house and acquired thrown away, since several are incredibly friendly. Also they have this thing about abdominal worms. And in those days China had not been as modern as now so stomach worms would have been a problem. Fleas aren't a really problem because they may have tile flooring surfaces and solid wood furniture.
Felines and mankind have been moving into harmony for many years but that has not always been the situation. There have been times when felines have been almost destroyed in the name of God. And what took place the Black Death reigned supreme for a lot longer than it will. So we will go back to the beginnings of recorded record to enough time of the pharaohs of Egypt. Here cats were revered as Gods and many were mummified to previous for eternity. Because the pet cats guarded the grain warehouses and wiped out the rats and mice that given on the grain. Therefore minimizing famines, which were the curse of Egypt. It had been illegal to destroy cats in those days, like cows in India today.