While in general you're right, deer aren't a great example. Deer populations in much of the US are actually higher than they historically would have been, large

While in general you're right, deer aren't a great example. Deer populations in much of the US are actually higher than they historically would have been, largely because predator populations have been artificially and dramatically constrained. Most deer predators, but especially gray wolves, are also livestock predators, which has justified their population control.