This is not a complete list of everything that can go wrong with cats! They can acquire or inherit some health problems that are more serious than the ones I've personally encountered. Cat Sanctuary cats normally have the opportunity to live natural, 99% outdoor lives, but here are two reasons why I've sterilized cats, confined cats, or sent cats on to city-type homes where they'd be permanently confined and sterilized.
1. Vertical hunting. There is some evidence that this is a gene, possibly correlated with body shape; the old saying is that cats with shorter tails are less effective mouse hunters, more likely to waste their time chasing birds. (Vertical-hunting cats very rarely catch a bird. They catch insects, and often eat crickets and grasshoppers.) If you entertain cats by trailing a string or weed stalk along the ground, it's easy to identify the ones that chase the string and the ones that try to jump up and grab your hand. This tendency toward vertical hunting seems to be permanently hard-wired into about 15% of the cat population, occurring more frequently in some "families." Although these cats won't actually catch healthy adult birds unless they find a nest on the ground, and it's necessary to protect only a few ground-nesting bird species for a limited time, I recommend sterilizing vertical hunters.
2. Frequently catching birds. I'm a bird watcher and know the local species. If a cat catches one bird from a ground-nesting species, it's time to confine the cats for an appropriate length of time--grouse and songbirds usually need protection for about three weeks in spring.
If a cat catches a bird from a tree-nesting species, the cat will confess by vomiting, and it's time to watch the cats. If more than one of these birds is spending enough time on the ground to interest my cats, that means a disease is going around. Repeated exposure to the disease could harm the cats. In my area songbirds seem to be most vulnerable to aspergillosis, to which cats and humans are mostly immune...but nobody needs to go on eating fungus-infected meat.