The same reason it isn't covered with beavers, parsley or anything else: as soon as there is a large increase in the number of, say, flies in an area, the fly-eating population thrives and multiplies until there are so many fly-eaters that they have consumed almost all of their prey, then the number of fly-eaters starts to diminish due to starvation. Once there are sufficiently few predators, the fly population increases again, etc. etc.
species equilibria - its a big subject. Incidentally the film "The Matrix" classifies humans as a virus as we can't reach some form of equilibrium, we just keep expanding in numbers. (Makes you think hey?)