“Anxiety and depression would cancel each other out because people who are depressed usually stop caring about the things they are or would be anxious about.”
OK I understand your point now. I’m not a psychologist so I’m not equipped to discuss why they don’t cancel out. I think these two conditions are very complex, and I can see reasons why they they could actually reinforce one another, which would explain the prevalence of their comorbidity.
However you can’t escape from the fact that the Mesilas Yeshorim does say that Bitochon is the cure for anxiety, which contradicts the OP’s assertion, that was the main point of my post. If you reject my explanation fine, I personally think its a good explanation, but would be very happy to hear if you have another way of understanding the Mesilas Yeshorim.