Fans have always tried to imitate their favourite franchises with their own versions of their characters stories. I admit I did it once when I was young, I wrote my own V story which I called 'Resistance'. Before Warner Bros begin legal action, I didn't sell, it was just for fun for myself and never released, well, back then there was no internet. Well, the internet was about but hadn't yet taken off with the Web as its become now.
A group of budding film makers launched a kickstarter project and have raised over $1 Million to produce Star Trek Prelude to Axanar and for the amount of money that been spent, it looks very good, see the picture below of Vulcan. Its also attracted well known actors such as Richard Hatch best known as Capt. Apollo and Tom Zarek in the Battlestar Galactica franchise.
It was probably best to sticking to Star Wars fan films as Lucasfilm had been known to be supportive and not be so litigant with fan fiction. There is also the officially recognised starWars.com Fan Film Awards As any Star Trek fan will know, there's another film coming out next year, Star Trek Beyond which is also the fiftieth anniversary year of the franchise. Could the producers be worried that some people might get confused and see Prelude to Axanar and think that's the Beyond film? I suspect Paramount and the producers of Axanar will come to some sort of friendly arrangement without any court cast coming from it after all its the fans that keep the franchises going. More info at Hollywood Reporter