@Kolyo,
You make a good argument for some environments. I will accept that in an environment that is not adapted for domestic cats, they can cause a problem with native species that have no defenses against these predators. I was just reading about New Zealand which had just such a problem.
But I don't think your arguments apply to the US, or to Europe. Domestic cats have been part of the environment in Boston (where I live) since the 1600's. We still have abundant bird and rodent life. Domestic cats have been in Europe for more than a thousand years. The other species are adapted and live with domestic cats as they have for centuries.
I only half agree with your predator-prey argument. Sure, domestic cats have a steady food supply that is not dependent on the prey population. But these cats are limited, to a fairly small number, by the desires of humans.
Around here, there are fewer than one cat per house (with many houses having no cats). And, the range of these cats is limited to places populated by humans (you don't see domesticated cats in wilderness areas unless they are feral... in which case they are now part of the predator-prey cycle).
I think that in special cases, in environments where that for some reason have not adapted to cats... or where there is a species that is endangered, that domestic cats could be curtailed.
But in much of the world domestic cats are a natural part of the environment as they have been for centuries. The environment around them is adapted to work and nature does just fine with cats in the mix.