It sure seems like nothing good has come of this. The legal situation (as we the public are being told) seems to boil down to a "he said/ she said" thing; Paramount says that Axanar is profiting off of them. Axanar denies this.
It's not "he said/she said" when there's data to back up one side's interpretation of the situation. In Axanar's own annual report Peter's admits to drawing at least a 38K salary for his work on Axanar and building out a studio intended not only for Star Trek fan films but also other science fiction films (presumably commercial projects), a science fiction film school, and an Axanar themed convention. All of these admissions point to either financial benefit, which was one of CBS/Paramount's concerns as noted in the original filing, or an intent to benefit financially based on a derivative work.
Furthermore, the motion to compel discovery clarifies CBS/Paramount's position--and damages Axanar's--based on what appear to be the results of an audit shared during discovery (Podcast 40, commentary starts about 13:30). CBS/Paramount state that
It is undisputed that Defendants raised money from Star Trek fans to make infringing films...Defendants’ documents show that they have spent tens of thousands of dollars, raised from Star Trek fans, on personal expenses and salaries, including car insurance and tires.
And that's just using available documentation, which avoids the twist of reasoning required to make the Donor Store/Station look legitimate by claiming it's an extension of the crowdfunding donation/perk system instead of a store. (Links go to Axamonitor where the original documents may be downloaded).
In short, Axanar is hoping that (global) you won't pay attention to the evidence against them, much of which comes through their own careless and hubristic admissions and actions, and instead accept unquestioningly what they say. It might feel good to fall in with Axanar and accept the narrative Peters is trying to sell, but reality just isn't supporting that interpretation at this time.
The new fan film rules seem to have been created in response to this, and while Paramount is within their rights to decide how it works, I for one think that -- while there are some perfectly fine regulations -- there's some pretty harsh stuff in there. If I was into fan filmmaking, I would not make a Star Trek film under this system. I recall that the website page where this was announced was flooded with negative feedback, so I think its safe to say that it was instigated at the cost of goodwill from the fanbase.
I suspect the new fan film rules have been under consideration for some time and were the result of the collective behavior of the larger fan film production groups. While Axanar pole-vaulted over the line between "fans playing" and "commercializing an IP you don't own", some of the other groups may have been getting too close to it for CBS/Paramount's comfort. Axanar just showed how some people will use everyone else for cover while they run with every inch they're given.
Fortunately, CBS/Paramount are unlikely to have hurt themselves with the fanbase as fan film fans do not equal the Star Trek fanbase. They are a minority of a minority.
The sad thing is, is that this all sprang from a fan film production, something that's supposed to celebrate the source material in question, be a way for fans to connect with the franchise sandbox, make it personal, and share something they love with other people in a way that has their personal touch. It's a tragedy, no matter which way you slice it.
It would be very sad if it sprang from a fan film production. Instead Axanar was a "fully-professional, independent Star Trek film." Therefore, I would say what is really sad is that Star Trek fan film fans were taken advantage of by a man who decided his next career would be as a Hollywood producer/studio owner and that the best way to go about that career change was to parasitize a popular franchise instead of paying his dues by creating original material.