Another thought to consider.
Deer and other prey animals are what they are because of their ability in the long term of dealing with whatever adversity comes their way.
Those able to stay vigilant and avoid being eaten by a predator might be more apt to survive and pass on their genes and teach their young some traits. Those that cannot might be more prone to being eaten.
In time, the "weak" ones, in this case those not vigilant, or quick, or green with brown dots (camo) or whatever advantage that occurs, are gone and only the "strong" remain. The age old story. Change is a constant and the herd is always changing.
Take away some adversity, say, top line predators, and that need is no longer important, no longer a deciding factor. Those without the "strong" advantage are no longer at a disadvantage. . for that particular adversity, and their genetic line can again flourish.
Deer will be here without predators. There will be other adversities to keep them in check, if we let them happen, but if you take away the wildness of a deer, is it really the same animal ?
Hunting a tame deer (neighborhood deer) in my back yard just doesn't sound appealing to me.
Additionally, those extra deer / elk etc affect their world to, like people on earth. Too many will eat too much and not just eat themselves out of house and home, but change their world.
Here we go again, those plants that are vigilant (yeah right), or that can grow faster, or higher, or that contain some chemical deterrent (natural GMO ?) might not be eaten and thus live to pass on genes, while the others won't. . and the forest changes because of that.
ChuckC