Maybe the reason I object to anxiety as a trope in cultural studies is because I suffer from an anxiety disorder which can be extreme at some moments. I suffer from GAD, or General Anxiety Disorder. The treatment I am doing now say that you shouldn't struggle against anxiety, or manage it, but accept it with compassion toward yourself. I am in the early stages of this, but the idea is that the main problem is trying to control or eliminate anxiety rather than accepting as a normal part of life. This attempt to control could work in the short term but creates a feedback loop that ends up making you a slave to your fear of the fear itself. Instead, you have to meditate and do other mindfulness techniques so you can accept your feelings as what they are.
But anxiety in cultural studies is about things people don't like. So, instead of saying people don't like the loss of social and cultural distinctions, you say they are anxious about it. Maybe so, but the claim seems larger, more mysterious that way, but how do you prove an anxiety (as opposed to simply something that bothers you or you don't like)? It's a kind of psychoanalysis of culture, but where the problem might be evident and on the surface rather than concealed.
I guess there are cultural "anxieties" and fears too. What I object to is the almost automatic and somewhat thoughtless recourse to this trope.