There is an appeal to fan fiction if you really love the universe and/or characters and want to somehow expand on some themes or ideas that the original writers seem to be missing out on (and often times for good reasons). But I still think fan fiction should be a step and not a stopping place for a writer. Unless you plan to become a writer that does scripts or novelizations for Star Trek, it's worth exploring the possibilities of your own imagination instead of depending on someone else's.