Yes, Cluin. Didn't the Europeans forego their attempted annihilation of small felines and start encouraging their proliferation because of the bubonic plague being spread so wildly by rats and mice?
Greg, if the wilde beasties higher on the food chain were not taking their share of the small rodent population, do you really think human society would just let the little critters run rampant and live long, healthy lives? I don't know that being devoured by a cat is as horrible a death as succumbing to rat poison.
BTW, the death of predators in nature is often slow and anguished, by starvation. The prey usually die more quickly.
In any event, it's not always a matter of OUR ranking wild animals in order of their value. Nature tends to establish the food chain largely on her own terms.