Much depends on your definition of "good", I expect.
Even setting aside the possibility of unforeseen negative side-effects of the change to ecosystems, etc., it's not clear to me that minimising human sickness is an absolute "good" that outweighs any other effects, and it's not clear how we should evaluate the deliberate extinction of another species.
How many human lives must be saved to justify an extinction? (Of course, those human lives aren't really "saved" in a long-term sense; they're still going to die, just from some other cause. Meanwhile, the extinct species remains permanently extinct.)
How many species can we justify eliminating in order to stop a given disease? One? Tens? Hundreds? Thousands? Does the answer depend on whether they're cute and furry?
