I wouldn't worry unduly about the number of birds they kill. Estimates of the numbers of breeding pairs of birds vary wildly, but 100 billion tends to the low estimate. And if they breed at say 10 chicks per pair, that means that each year, 1 trillion birds die if the population is roughly...
Not to mention my neighbour's pet pigeon that was ripped to pieces last year by an out of control domestic animal. I will not identify the species for fear of spoiling anyone's illusions.
Your average cat has no objection in principle to the ripping to pieces of live animals. It probably does...