Assuming humans did not exist, the main moral justification I see would be to prevent the unnecessary suffering of living beings. Of course suffering is a part of natural systems, but as living beings, we can identify with the discomfort of said suffering, and find it a moral imperative to limit suffering to only that which is necessary.
When natural systems can no longer sustain life, that life dies out. This can happen when there are no longer enough natural resources to support said life. But this does not necessarily happen quickly. The cause could be drought or famine or climate chane, resulting in lack of an environment suitable to life. This can cause the deterioration of a species to the point of disease, starvation, cannibalization, and other painful processes.
Let's take an example. Assume that some new disease affected a wolf population in a given area. Once those wolves died out, the lack of natural predators would cause other species (say, deer) to reproduce abundantly, and then overgraze, which would then affect the growth of forests, which then would affect the ecology sustaining a myriad of species that live in said forest. Assuming those species attempted to adapt by migration, they may be adversely affected by other species in a new region, or adversely affect those species themselves, setting off new chain reactions.
This is not a theory. This is a real problem affecting the northeast united states. Except it wasn't disease that killed off the wolves: it was humans.