A very good question.
Rewilding and other ecological restoration advocates use a variety of arguments. Some are utilitarian, and relate to the economic benefits of healthier and arguably more productive ecosystems, with more provision of the goods ecological economists call "ecosytem services," such as clean water, pollution control by wetlands, and so on.
Some motivations are extension theories, whereby we decide that ecosystems have intrinsic rights to exist, "untrammelled," as it says in the 1964 Wilderness Act, by the hand of man. They become, in a sense, individuals before the law, and as Christopher Stone said, they have "standing."
I think the best arguments for restoration are deontological (but I would, since I already know myself to be a dutiful deontologist).
We decide to restore ecosystems because we have duties to the planet, to God if we believe in one, and to human posterity. We have duties to not entirely destroy every beautiful and living thing on this earth, not to chop up every wilderness and feed it as raw material into the ever-open maw of commerce, not to alienate very kind of creature, including humans, from some relatively safe spot on this earth where they can do their best to live out a free life, as nature intended.
I find this last entirely believable, good, and true. This short piece is therefore a polemic, if a socratic one. But this is only my opinion, not my teaching.
Ethics students, discuss!