Yes, good point.
Most prey species will breed until they destroy the food supply in their environment and then the population crashes, with most of them starving or dying of disease. Deer are a classic case - left alone they will always multiply until they consume all the browse, then die off to a minimum population while the vegetation replaces itself over a few years, then repeat the cycle.
The "average" carrying capacity of a piece of land might be 10 deer, but you'll never have 10 deer on it. You'll have 2, then 100, then 2, then 100, etc. And those 100 are pretty skinny, miserable, and disease and pest ridden.
Predator populations follow the prey; as prey increases so do number of predators, and vice versa. It's not clear that they have much real impact, perhaps they slow the cycle somewhat.