Hey Natalie! The way that this phrase is worded seems... wrong. Audacity is like the willingness to be rude, but being "concerned" is the opposite of rude. The phrase would have to very sarcastic for it to make sense (to me). One example I can think of: Person A: "I don't think anyone should tell me how to eat healthily" B: "Oh, I wouldn't have the audacity to be concerned about your health" (sarcastically)

In a casual conversation I think this is rarely, if never, used. You could just say "why aren't you worried?" This would probably be used in politics where people are obligated to use a high level of vocabulary.