OK, here's a thought I've had in recent months, since I've been following the Axanar updates which are posted almost daily.
Alec Peters has used some of the proceeds from the kickstarters and such to build an (independent) movie studio. Axanar Productions as a studio has become a pretty extensive facility, with the most recent addition being construction of one of the largest green screens outside of Hollywood proper.
So while they may not be earning a profit from the movie itself, the props, facilities, etc. that they are building can be used to generate a profit for other endeavors, and it's pretty obvious to me that Alec is thinking beyond Axanar based on some statements he's made in recent months. As such, it could be argued that the Axanar team is, in effect, profiting from use of the Star Trek copyright.
That being said, I think that CBS's long history of allowing fan productions does call this matter somewhat into question. Why should only Axanar be targetted, but not other productions, i.e. selective enforcement of the copyright? It is CBS's copyright, but if they are going to draw the line with Axanar, then really all other Trek related fan efforts should be addressed as well.
Myself, I think that CBS would be wise to settle with the Axanar team on some sort of 'use of copyright' agreement. This could turn Axanar into a for profit venture, but then both sides could benefit (CBS could then share the revenues generated with Axanar studios). Sure, Axanar is the 'infringing party', and Alec has made several efforts to negotiate in good faith with CBS (at least according to the press releases I've read), but I think that the CBS legal team would do better by setting some reasonable terms for 'use of copyright' rather than shutting this down entirely.
Of course, movie studios aren't noted for making the best decisions, and we have plenty of examples of things in 'copyright limbo' because the rights to some game or something can't be secured or even in some cases clearly established. So, I'm not overly optimistic about Alec Peter's chances to move forward on this. I do hope that an arrangement can be reached, because at this point that is the best chance for Axanar to move forward.
We saw Enterprise killed off by Paramount (just when it was getting interesting), because they chose to terminate the series instead of allowing the production to move to Canada at a much cheaper cost to produce. There was a proposal on the table to do exactly that, but because Paramount studios wouldn't be doing the production in Hollywood, that proposal died a quick death. Since they didn't think it could be profitable enough/generate the numbers they wanted if they continued to do it onsite, they killed Enterprise off.
MGM understood this very well with the Stargate franchise by doing the production in Canada, which is why Stargate was so long lived I'm sure. With 10 seasons, plus movies and several spin-offs (5 seasons of Stargate Atlantis, and the short-lived SGU, oh and wasn't there a cartoon too?), the Stargate license did very well for MGM.
So yeah, CBS/Paramount making this move now doesn't surprise me, but it'll take a herculean effort by the fans to change the course CBS is now on. Time to make some noise!
My two cents, anyways...