As you learn more about most systems, the likelihood ratio should likely go down for each additional point of evidence.

I’d be interested to see the assumptions which go into this. As Stuart has pointed out, it’s got to do with how correlated the evidence is. And for fat-tailed distributions we probably should expect to be surprised at a constant rate.

You might be also be interested in “General Bayesian Theories and the Emergence of the Exclusivity Principle” by Chiribella et al. which claims that quantum theory is the most general theory which satisfies Bayesian consistency conditions.

By now, there are actually quite a few attempts to reconstruct quantum theory from more “reasonable” axioms besides Hardy’s. You can track the refrences in the paper above to find some more of them.