I don't see any positive aspects of the "fan" feature, either gameplaywise or communitywise.
Making it private automaticly deactivates the whole purpose of being a "fan". Make it public only but for what? I doubt that Cookiezi would care about ANY of the so called "fans". If you do care about someone even for a bit, you have a friendlist for that. Anyway, in the end, what is the purpose of it?
In my opinion it can, as said above, make the things maybe even worse with people trolling like "haha you are a N00b fan of X". If you do really want to show everyone what a true fan you are, there are tons of way of doing that. Write that on your profile page into "interests" or "User Page", or make your own Facebook Fanclub page of X person and make a link in your profile for it. You don't need a "BIG BANNER" on your front profile page saying "I am a X fan".
Concluding, making it private is totaly useless since it will be kind of "haha no one knows that I am a X fan". To maybe show how popular someone is just check the replay watched by others and you will see who is the "top" person "followed" by others.