The point is that those facts are irrelevant, in much the same way that it's irrelevant to bring up that tomatoes are botanically a fruit when discussing fruit salad.
Nowhere does the article say sleep deprivation isn't bad for you in myriad ways. Rather, it's making the point that, for people who are sleep deprived due to insomnia, stressing out about your lack of sleep compounds the problem, by making it even harder to fall asleep. So one way to solve insomnia-related sleep deprivation is precisely to not make a big deal of it, and remove the anxiety component.
Climate change? Air pollution? If you don't see how these are completely different problems that are completely unrelated to your mental well-being, I don't know what to say...
Of course, worrying about _anything_ creates stress. But that's as far as it goes: Worrying about air pollution creates stress, but stress doesn't create more air pollution. Worrying about climate change doesn't make climate change worse.
The problem is closing the loop — worrying about sleeplessness produces stress, which then goes on to make the sleep disorder even worse. Same with weight loss and emotional eating.