Feral animals of all types cause serious problems. Feral cats are getting so bad in some places in this country that the state has to go in and capture and destroy them. Most feral cats are ones left ababndoned by families, and include cats that have even been de-clawed (the ultimate in cruelty). Where one feral species thrives, another native species (or several species) dies. To maintain a balance, and to help the native species survie, the feral animals have to be eradicated.
That and cats are small , smart and quick, thus lending themselves to improve my marksmanship.
But seriously, not only should hunting feral cats and dogs be legal, there should be a bounty.