My husband and I have this conversation about twice a year, which how often we find ourselves at Chick-fil-A. As far as food goes, no, I don't believe it is "worth" the high "fast food" price. That said, Chick-fil-A is the most pleasant fast food environment I've ever experienced.
Their customer service is outstanding. They go out of their way to take care of children (a huge plus for us). The restaurant is beyond clean. They think of so many things that no one else thinks of (bibs, sani-wipes in the kids' area, cups of cheerios in the morning while you wait for your food with little ones, Tuesday night art night). So in this regard, I still claim to love Chick-fil-A and when we are desperate for a night off of cooking, we'll still hit it up once or twice a year.
(I do remember we had it in our student union building in college and so I could pay for it with my meal plan money. Then, it always seemed worth it. Funny how my perspective has changed.)