Inconsistency is a good problem to have. I think for most people the creativity problem is at an earlier stage - they just can't come up with non-boring stuff, consistent or not.
Though I don't think the analytic function metaphor illuminates much, I do agree with your premise. I think that so long as what is created makes sense in the world it is created then it is believable. Of course, being believable is not always desired by a writer but that escapes the bounding of the post.
That is part of the draw of fantasy worlds, that they are not our own permits a greater range of believeability, within the world itself. Taking something from Star Wars or LotR and placing it, without the appropriate context, (which would be, to its fullest extent, the rest of the respective fantasy world) into our world will render it unbelievable, but that is okay, so long as it is believable within its world.
(And yes, technically Star Wars takes place in our world just far away and long ago, oops)
It confuses me a little that you're proposing a broad question ("is it okay for X to do Y?"/"should X feel free to do Y?") and then answering with a personal preference ("I personally would enjoy it more if X did Y"). Surely there are a lot of people who don't mind or even prefer inconsistent axioms in the literature they read, and it seems fine for writers to create content catering to their desires.
Apologies for the clickbaity title. A question that I've often come across is how much freedom should science fiction writers have in world building. Is it permissible to take liberty with the laws of physics? Is it OK to depict anthropomorphic AIs?
I hold the opinion that fantasy and SF writers should feel free to create unrealistic pictures of the future, so long as they do it consistently. They should feel free to conjure up worlds that are not probable, like creating an analytic complex valued function, which is partly obfuscated. However, the world is an enjoyable experience only if the culture and plot are entailed by the axioms of the world. To continue the forced analogy further, the analytic function defined on part of the complex plane is really interesting when the occluded parts of the function are exactly what one would obtain by analytic continuation. In less pretentious terms, validity is more important to me than soundness. You may decide the axioms of the world, but the culture and plot must follow as an inevitable outcome of the axioms.