Enjoying something and doing it for the fun are two different things. Psychology of the muse aside, it’s like the difference between taking fanfic writing seriously and treating it as just a hobby where you can blow off grammar and good taste.
When people start throwing around words like fun or happy that don’t really seem to refer to much, compared to fine old designations like joy or sorrow, I mourn the loss of the true meanings of words. Especially in the realm of emotions, good words are slipping away into a morass of vague synonyms. I fight back with the dictionary; there’s nothing like a controlling legal authority in these cases, and mine is Webster:
The relevant idiom is to make fun of, which is to ridicule, and in fun, which is, not seriously. I can only repeat that fun and games are not what I’m after here. If you told me you were after joy, or honor, or love, I would know what you were talking about, but fun? It’s an empty bit of slang, or as the dictionary puts it, it’s colloquial.
I usually get into this discussion over another word, happy. Happy means fortunate, which is obvious from the word itself. (See, for example, perhaps and happenstance, words that refer to chance.) When you extend it to an emotion that presumably results from the circumstance of good fortune, you get a weak word and a lot of people wishing they felt happy when they ought to be wishing to be happy. But people shy away from words that really say something, like joy.
So no, I’m not in it for the fun. You can keep the fun, and I’ll take the joy and the sorrow both. I still come out ahead.