I think one of the reason why there were few cats around is basically because they used to consume them. And once in a while the restaurant kitten catches would grab an kitten they could find and take them back to the restaurant. I remember seeing felines in glass exhibits out the front of the restaurants. But somewhere within then and now they prohibited eating pet cats. So cats are actually not on the menu and now there are pet cats everywhere. Many of them began in someone's house and got thrown away, since many are very 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 are not really a problem because they have tile flooring surfaces and solid wood furniture.
Pet cats and mankind have been residing in harmony for quite some time but that hasn't always been the case. There have been times when felines have been almost wiped out in the name of God. And what occurred the Black Loss of life reigned supreme for considerably longer than it should. So we will get back to the origins of recorded background to enough time of the pharaohs of Egypt. Here felines were revered as Gods and many were mummified to last for eternity. Because the cats guarded the grain warehouses and killed the rats and mice that fed on the grain. Therefore lowering famines, which were the curse of Egypt. It had been illegal to eliminate cats in those days, like cows in India today.