It's mostly a safe assumption for wild birds, too, though, and for similar reasons. It's easier to find a young oblivious bird, or a desperately hungry bird taking a risk in a less protected feeding spot, to snack on if the population is healthy, and when the population is smaller there is less predation because they all fit within the safe feeding areas. If a wild population is large, there will be more deaths due to disease (which spreads faster in crowded conditions), and more deaths from hunger as they outstrip their food sources. If the population is kept in check more by predators than by disease or hunger, it's generally not a threat to the size of the population.

There are some specific locations that have certain animal populations actually under threat by domestic cats, but those are almost all ground animals and not birds.