Validity>Soundness in Creative Writing

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.