Animals evolved to keep each other in check. If you remove one animal, but not its prey, then the prey can cause an even greater loss of biodiversity by excessive proliferation. In the case of Yellowstone’s wolves, their absence allowed elk to proliferate. Elk then ate too much vegetarian, which prevented forests from developing. The lack of forest lead to a decline in song bird and beaver populations. The decline in beavers lead to a decline in dams, which removed key habitats for other animals.
To flip your question on its head: the reintroduction of wolves was clearly beneficial for Yellowstone. What is the argument against reintroducing the wolf, or reintroductions in general?