Engaging in mindfulness implies changing what you think about, or, where your focus is. This can be therapeutic to persons who are suffer from anxiety and depression because it interrupts periods where negative thoughts dominate their consciousness and replaces them with periods where their thoughts focused on current circumstances that are generally benign or pleasant. For persons who don't benefit from such therapy…
Just as easily I could argue that being more mindful can mean becoming more aware of the anxiety that is present, and that clearing one's mind leaves more room for clear analytical thought. I think you are analyzing from an armchair, not from a meditation cushion.
That is why the tradition emphasizes constantly that "you are not your thoughts." Putting some distance between you and your anxiety helps address it as the meaningless reflex that it is.