Red-tailed hawks are pretty prolific at hunting squirrels in urban areas. There are even pairs nesting in Central Park in NY and subsisting almost entirely on squirrels. Peregrine Falcons also hunt pigeons in Urban areas and again there are dozens of pairs nesting in the NY City metro area. Predators generally tend to find an equilibrium with their prey animals in an area, so they're not going to completely eliminate their prey.
> The best available research indicates 95% of an average rural fox’s diet consists of meat, both hunted and scavenged, and mainly rabbits, rats, birds and small mammals. Insects and worms may constitute another 4% and the remaining 1% may consist of fruit.
http://foxproject.org.uk/fox-facts/red-fox-diet/
Probably because they would also not discriminate against taking a swipe at small dogs and pets. So people complain and now your suburb is free from foxes and coyotes
You can. They sell pellet guns at Walmart. Good ones that will kill a squirrel. From experience understand giving one to kids will likely end with a pellet through a window or through a shoe.