"Cats can catch only the birds which come close to the ground to feed, or nest. There are precious few bird species in urban areas which do that."

What nonsense! Do some research.

Another reason to keep a cat indoors is its own welfare. Cats outdoors get:

mauled by dogs and other cats
hit by cars
lost
stuck in high trees. It's not funny.
exposed to diseases such as giardia and feline leukemia
tapeworms from eating mice
bring fleas into the home.
kidney disease from lack of water.