My cats do NOT suck at catching birds. They catch everything. Mice, rats, squirrels, moles, voles, chipmunks, bats, rabbits, birds, even crows.
Today the dead critters on my doorstep are mice.
Yesterday it was birds.
The day before that bats.
The day before that voles.
The two orange boys hunt as a team, and the tortie mama hunts alone, but is the Mighty Huntress. When they were babies she used to bring semi-dead animals into the house and release them to teach the boys to hunt.
I also have one orange girl who is indoor only, and she hunts spiders and flies and centipedes.
We've had them for five years and they've killed thousands of critters.
You must have some very talented cats, because my cats (and those I have experience with) don't/can't catch birds except very rarely. They do a lot better with ground rodents.
That said, there's several scientific studies floating around that confirm my position - cats as a whole suck at catching birds.
Even if they didn't, by killing birds, they reduce the number of disease-carrying flying vermin that crap on my cars. (Yes, birds carry diseases transmitted through their crap).
I once had a yellow tom, who was indisputably the baddest cat in the 'hood. He even went after dogs, and whipped many of them. He caught every kind of vermin, too, and brought them for my approval.
Nice tagline. : )