The fact of the matter is we have long /wanted/ their response be to kill all the scurrying rats and tiny birds weren't exactly a concern compared to not dying.
Most rodent control in the modern era comes from modern building techniques and materials, as well as waste disposal networks, that keep rodents out of our buildings and away from human sources of food. Go to a neighborhood with well maintained buildings but no cats and you'll find fuck-all rodents. Go to a neighborhood with run down buildings and a million cats, and you'll find a billion rodents.
The excuses made for cats seem to nearly always be characterized by a lack of critical thought. Saying that is probably considered controversial, but so is the toxoplasmosis hypothesis.
The objective function that most human beings use is not "what animal kills rodents most efficiently", but "what animal kills rodents most efficiently and poses little harm to human beings most of the time". In my experience, most stray cats will likely run away from children and most stray cats will likely not initiate attacks against children. On the other hand, most stray dogs are more likely to do both of those things. As a result, cats get a pass for being less efficient rodent killers than dogs because they are also less likely to harm human beings.
See, I disagree. I do not believe that killing rodents is a serious consideration for most modern cat owners. There are cheaper, more efficient and lower maintenance methods of exterminating rodents than cats. Most cat owners own their cat as a pet and think nothing of letting it terrorize the neighborhood birds because it's cute. Talk of rodent extermination is a post-hoc justification for their behavior.
And face it, every bird pair has half a dozen chicks each year. Next year the bird population is about the same. That means, most new birds are going to die in the first year. Cats are just a part of that.
Same can be said for humans.