Would it be any tougher than writing such a book, but set on Earth?
As long as someone is capable of writing how humans behave in real life, they should be able to write how human-oids behave. Its just a matter of writing what an Earth writer would, but setting it in the mountains of Qo'noS, or the back streets of Qu'vakh City, or whatever. Basically humanoids in Star Trek, are humans - they have human psychology, or else characters like Worf or Tuvok would never work - if they were not driven by the same psychology as humans, they would be utterly un-compelling to the viewer - therefore a good observer of humans should be a decent writer of Klingons, Cardassians, Romulans, etc.
Ah, but I don't want my Klingons, Romulans, Cardassians etc to simply be humans telling human stories set somewhere else. They can be that to a point, but I want each to be a distinct form of being (and the novels have indeed helped make it so). I wouldn't be too thrilled with a story written as part of this hypothetical project that was simply a human archetype but with the names changed so it fits in on Qo'noS. Yes, you're right of course that TV Trek
does often do that (most of its aliens are humans to all intents and purposes)- and it's not a bad thing by any means, for TV or even some novels- but in literature, where there's more room for worldbuilding, I prefer my aliens to feel alien.
They can still be used to illuminate humanity, and, as you say, basic psychological similarities are necessary (and I guess logical given shared humanoid biology/environmental requirements). However, to me, simply telling a Cardassian or Andorian version of an Earth saga would miss the entire point of attempting to craft these tales as fiction from the alien's own viewpoint. That's what I found so intriguing about this hypothetical project- most Trek stories (naturally)show us alien societies and alien viewpoints (to differing degrees of "alien" as you acknowledge), but they are always geared directly to a human readership (obviously). With this proposed idea, however, you'd have to work to overcome that. It's not simply "how would an Andorian see the world?", or even "how would an Andorian explain or describe an Andorian way of thinking to outsiders?"- both of these questions have been asked and explored by multiple authors- here, the question would be, "how does an Andorian hypothetically take an Andorian mode of thinking and apply it to imaginative works of fiction aimed at other Andorians?". That's a very complex idea, bringing in a whole new layer of author creativity and cultural illumination. I believe it would be challenging, but the writers involved could really, really make it worth it.