I believe 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 feline they may find and take them back again to the restaurant. I recall seeing felines in glass exhibits out leading of the restaurants. But somewhere within then and now they prohibited eating cats. So cats are actually not on the menu and today there are pet cats everywhere. Many of them began in someone's house and got thrown away, as a general rule are incredibly friendly. Also they may have this thing about stomach worms. And in those times China had not been as modern as now so tummy worms is a problem. Fleas are not a really problem because they have got tile floor surfaces and solid wood furniture.
Cats and mankind have been surviving in harmony for quite some time but that has not always been the situation. There were times when cats have been almost destroyed in the name of God. And what happened the Black Loss of life reigned supreme for considerably longer than it should. So we will get back to the beginnings of recorded background to enough time of the pharaohs of Egypt. Here felines were revered as Gods and many were mummified to previous for eternity. Because the felines guarded the grain warehouses and killed the rats and mice that fed on the grain. Therefore reducing famines, which were the curse of Egypt. It was illegal to destroy cats in those days, like cows in India today.