I just don't see "not having faith" as being the entire cause of a mental illness. Many things can contribute to mental illness or make it worse, but when anxiety is at a clinical degree it's not "not having faith", "not exercising", "not eating right" that's the perpetrator. Exercising, eating right, getting sun, talking to God, reading the Bible.... these are all things that can greatly help, certainly. But unless the root cause of the disorder is the lack of these things, then doing them will not cure you, short of a literal miracle.
There is also, though, that not all depression is a depressive disorder, and not all heavy anxiety is an anxiety disorder. There are specific criteria's that are supposed to be met before they are considered to be disordered. Probably most of the time anxiety and depression are reactions to adverse situations, rather than an inherent chemical imbalance that will never go away. Or they are acquired after going through something traumatic, and stick around in the form of trauma responses. (Important to note that not everyone who goes through traumatic events has lasting trauma in big ways. They might be said to have "little t" trauma in that the event affects them and the way they live in small ways, but not "big T" trauma where they are greatly affected for life.)