Please expound on how any of your points cannot be applied to domesticated animals, please.
For example, feral cats fit all of your points, but they can be successfully domesticated. If cats were left in the wild and prohibited access to human, many would die of preventable disease. And yes, a feral cat is a very wild animal and cannot be domesticated successful, but offspring can easily be turned around while small. Disease of cats can for the most part be controlled with modern medicine.
I also find it insulting that you think that man is too dumb to take care of the health issues.
From the disease perspective it's not a matter of whether you can tame the damned thing. It's a matter of disease control. A deer population, for example, doesn't have veterinarians looking after it, and no disease control methods should something break out. You wouldn't bring a plague victim into your home, would you?
Sheesh. Do your own damned thinking.