The Simpsons is already way ahead, with a similar scenario (lizards getting rid of the menacing pigeon population) :
SKINNER
Well, I was wrong. The lizards are a godsend.
LISA
But isn't that a bit short-sighted? What happens when we're overrun by lizards?
SKINNER
No problem. We simply unleash wave after wave of Chinese needle snakes. They'll wipe out the lizards.
LISA
But aren't the snakes even worse?
SKINNER
Yes, but we're prepared for that. We've lined up a fabulous type of gorilla that thrives on snake meat.
LISA
But then we're stuck with gorillas!
SKINNER
No, that's the beautiful part. When wintertime rolls around, the gorillas simply freeze to death.
SKINNER Well, I was wrong. The lizards are a godsend.
LISA But isn't that a bit short-sighted? What happens when we're overrun by lizards?
SKINNER No problem. We simply unleash wave after wave of Chinese needle snakes. They'll wipe out the lizards.
LISA But aren't the snakes even worse?
SKINNER Yes, but we're prepared for that. We've lined up a fabulous type of gorilla that thrives on snake meat.
LISA But then we're stuck with gorillas!
SKINNER No, that's the beautiful part. When wintertime rolls around, the gorillas simply freeze to death.