I like your point but not your example.

Suppose (because you're a computationally-limited Bayesian) that you only include in your model the N highest-probability hypotheses. That is, you include A, B, C, in your model, but you neglect Z - that is, you put zero probability on it. (We can make Z's pre-evidence probability arbitrarily small, to make this seem reasonable at the time.) When one, or even N balls turn out to be labeled Z, the model (due to the initial zero probability on Z) continues insisting that the balls came from one of the initially-specified hypotheses.

That isn't just a computational limitation. It's an outright bug. Something that assigns 0 to Z is just not even an approximation of a Bayesian. A sane agent with limited resources may, for example, assign a probability to "A,B,C and 'something else'". If it explicitly assigned an (arbitrarily close to) 0 to Z then it just fails at life.