Well, there are in my opinion. Worth remembering that when I say "merit", I mean that there is some level of argument, not that they will necessarily win.
First you have fair use. Is it an argument that will succeed? I don't think so. But there is nonetheless some argument that Axanar is not a direct copy of Trek and therefore is transformative. The reason I don't think that will succeed is that Axanar still relies on the core heart and hallmarks of Trek. I've said this in here since January. In layman's terms, if it walks like a duck and talks like a duck, etc. But there is nonetheless an argument. It's like the example I Gave above from my own case when I said my opponent's application likely won't succeed. But she will be unlikely to get penalised by a judge as long as there is some level of credibility in her application.
Second, even if they lose on fair use, they will have a duty to try and mitigate the level of damages ordered against Peters & Co, and in such circumstances the fact that the studio hasn't gone after productions like New Voyages might come into play and might be an argument that impacts the level of damages. As a lawyer you have to be conscious not just of what is happening in the here and now, but what could happen in any number of scenarios that could possibly play out.
It's only really if they made an application totally and completely devoid of argument that you could say they are advancing a vexatious defence.