Why does she carry the inhaler with her? Because she might need it, and can't predict when. Why would you get a TUE? Because you might need it, and don't know when.
It was enough of an issue to get three TUEs that would cover him in the 2009 season.
Like Froome, Wiggins wrote a book about his racing, in which he never mentioned asthma. Given how his own later statements revealed that he had a desperate need for certain medications, that is quite curious.
If a rider has some medical condition that can be treated without substances that are known or thought to be performance-enhancing, then that is his business, and maybe he doesn't want to talk about it. But when you are a TDF winner, and writing a book about how remarkable and inspiring your life has been, and you have a condition that is treated with a drug that is potentially performance enhancing, how can you not mention this?