We've seen this before: Efforts to control one aspect of a natural evironment resulted in unforseen, and unwanted consequences.
In this case, "the decision to eradicate the felines from Macquarie island allowed the rabbit population to explode and, in turn, destroy much of its fragile vegetation that birds depend on for cover, researchers said Tuesday." -
Source
Similarly consequences have been observed over the years as various species were introduced to control a "nuisance" animal, only to discover than in the new environment, the control species wound up being the nuisance, or worse. At times, it's resulted in the elimination of a native species.
In forest management, we observe that prohibitions against allow natural burning to run it's course, or to replace it with controlled burning as a substitute, can result in entire forests that are ripe for wildfire. Both Yellowstone as well as a large area in the Rockies to the West of Colo Springs/Denver area have been decimated in years past.
Naturally, some argue that measures weren't taken far enough: "What was wrong was that the rabbits were not eradicated at the same time as the cats," University of Auckland Prof. Mick Clout, who also is a member of the Union's invasive species specialist group. "It would have been ideal if the cats and rabbits were eradicated at the same time, or the rabbits first and the cats subsequently."
But it turns out there are mice on the island, as well, which thrive on the vegetation if the rabbits are removed.
Since dogs eat mice, cats, and rabbits, yet aren't exactly the greatest bird catchers due to their lack of claws, and don't eat the grass, perhaps it would have been better to simply introduce a fourth mammal on the island....
Of course, "We believe that the process they are going to follow uses best practice for this type of work," Ingwersen said. "And that all possible ramifications have now been considered."
Yeah. Right...