A lot of cities and towns have 'leash laws' for dogs, and restrictions for cats as well.
One of my neighbors actually had a dispute with another neighbor after the cat one owned jumped on their new truck and scratched the paint. Not only did the cat owner have to use their home owners insurance to pay for damage to the truck but they were fined by the town for not properly securing the cat to their own property.
When people don't spay/neuter their animals they'll breed- cats can and do turn feral, which can cause overpopulation problems, destruction of property and at times environmental unrest when fleas, disease and illnesses are spread.
It can also cause an overload with local agencies- police being called when there are 'strays' or damage, city workers being called to pick up the deceased off of roads- animal control agencies work harder and therefore use more tax payer funded money in housing, caring for, euthanizing and disposing of the unwanted, hurt or stray animals.
Of course, there comes the point of protecting the animal, may they be dogs or cats- from injury, disease, predators, unruly individuals and others of their kind.
I guess people want to 'protect' their investments as well. Or, maybe it's their own money, LOL! Injured pets co$t to repair and give medical attention to, something that people don't always have immediate funds to attend to. A healthy, relatively "safe" animal is generally less costly to have which in the end will be more beneficial to all involved, and especially when animals reach a more advanced age and need additional funding to better their existance overall.