> It makes an unbounded number of future predictions

nit: it's trained on finitely many samples.

> So counter to your claim that "It doesn't trivially imply that the model would learn sensible distributions under uncertainty" I think you need to consider what it means to optimally update a posterior under the global minimizer of the true conditional distribution.

Huh? That's not counter to anything I said. All I said was it's not trivially implied.