My reply: Doh! Cats are not a health issue? Read this from the Asthma and Allergy foundation of America.
Allergies to pets with fur or feathers are common, especially among people who have other allergies or asthma. From 15 percent to 30 percent of people with allergies have allergic reactions to cats and dogs.
People with dog allergies may be allergic to all dogs or to only some breeds. Cat allergies are about twice as common as dog allergies.
More: "If the cats are simply removed, others will come in from outlying areas and take over the now vacant territory."
Pardon me for correcting you. You seem to be granting ownership of our ecology to a pet species. If you take away one cat or fifty million it will relieve their hunting pressure on our natural fauna and allow them to reclaim it. Should pit bulls and poodles be managed in colonies outdoors running free? I don't think so, and neither should cats.