They can serve, through powerful and emotive storytelling, to help make readers more conscious of what's at stake as the world warms degree by degree. These novels can be wake-up calls, alarm bells, warning flares but they need not be depressing. I prefer to see them as calls to action, after the last page has been turned.
In the end, cli-fi is a literary cousin of sci-fi. The difference between them is that sci-fi is more speculative and escapist and entertainment oriented, while cli-fi is based on reality and real science. That's what sets the two genres apart.