Ah, interesting link. I think I ran into some confusion since 'rational' and 'Bayesian' are somewhat overloaded terms.

When I think of Bayesian analysis, I always think of Bayesian models which attempt to model uncertainty and always have a posterior distribution (spread) of outcomes.

For example, in the Dutch Book page, instead of having a point-prior (P=0.51 (delta on P=0.51?)), each degree of belief could have some (different) distribution which could yield a posterior with a distribution and change the math here.

Yeah well there's a difference if you're estimating a parameter or predicting true/false on an event.

Not sure about that, think about the case of (Bayesian) logistic regression.