I wonder what makes them not cost effective. The rink is rented for a certain price. Do the judges get paid per event or per day? What are the variable costs at ANs? Besides, the more people enter different events, the more money the competition makes.
First, you have hourly ice costs. You must rent the ice by the hour, and in some rinks that can be quite expensive. This means you are renting ice for practice ice as well as competition ice. For ANs, this likely means all day for at least 4 days (2 sheets) for competition, plus practice on Tuesday and the practices during the week as well.
Next, you have to fly in officials. This means judges, music, accountants, tech specialists, etc. They have a per diem as well as airfare, hotel, etc. If there is no shuttle service by the hotel, you either need to provide it (which may mean renting a car or van) or they have to get rental cars.
You may have IJS equipment rental costs. You have judges gifts, competitors gifts, and hospitality costs if you can't get that stuff donated. You may need to pay for advertising and publicity. Then there are costs for the competitor's party as well.
If I recall correctly, entry fees generally go to US Figure Skating. I don't know if the host club gets a certain percentage or they get something outright, but I don't think the full entry fee goes to the host club because it's a US Figure Skating event.