If God is preserving people, how could famine and disease and natural disasters happen, or how could cultures die out? I do think you’re reading a bit too much into a poetic passage, but it is a good reminder that God does value animals.
Another I like is the last verse in the book of Jonah:
11 And should I not have concern for the great city of Nineveh, in which there are more than a hundred and twenty thousand people who cannot tell their right hand from their left—and also many animals?”
God held off destroying an entire city, and while he was primarily concerned for the people, he was concerned for the animals as well.
Preserving is not equal to not going extinct as a species, since the writer and audience had no concept of extinction, or species for that matter. To read it that way is to inject modern concepts into an ancient writing that is not addressing that subject. I think the thought of the writer was along the lines of being thankful for God’s provision for both us and creation. And while it falls near to also reading modern concepts into the text that is not there, one way God could provide for the preservation of both people and animals, is to provide a means to adapt to a changing and challenging world, i.e. evolution. Thus the wolf is preserved in the domestic dog, etc.
We’re it not for a means of adaptation, life for all might be in jeopardy.