Seeing what happened to fan films, I hope people don't put Trek fan fiction up for any sort of publication or else that'll soon come under ridiculous restrictions as well.
Oh, that's been going on for years already, and the lawyers do crack down on it regularly. But prose fiction doesn't have anywhere near the profit potential of films, so it doesn't get nearly as much attention.
And the restrictions aren't ridiculous. Strictly speaking, all fanfiction is illegal. It's an act of generosity on the studio's part to tolerate its existence at all. But if people abuse that generosity by trying to make a profit and compete with the studio, then they've crossed a line and the owners of the property are entirely within their rights to rein in such excesses. The fact that they still tolerate it at all, even after some have abused the privilege, is still extremely generous. (Doug Drexler recently said on Facebook that it's like someone letting you drive their Ferrari once a week.) People who sell fanfic for a profit already get cracked down on routinely, while people who respect the rules and keep it nonprofit and recreational are still allowed to indulge themselves. The fan film rules are just a version of the same principles already enforced on prose fanfiction.