I’m not sure what the problem is, nor why you connect Bayesian approaches with “how some agent with a given expected utility should act”. There is a connection between those concepts, but they’re certainly not the same thing.
The Bayesian approach is simply that you can update prior credences of hypotheses using evidence to get posterior credences. If the posterior credence is literally zero then that hypothesis is eliminated in the sense that every remaining hypothesis with nonzero credence now outweighs it. There will always be hypotheses that have nonzero credence.
I’m not sure what the problem is, nor why you connect Bayesian approaches with “how some agent with a given expected utility should act”. There is a connection between those concepts, but they’re certainly not the same thing.
The Bayesian approach is simply that you can update prior credences of hypotheses using evidence to get posterior credences. If the posterior credence is literally zero then that hypothesis is eliminated in the sense that every remaining hypothesis with nonzero credence now outweighs it. There will always be hypotheses that have nonzero credence.
See my response to a similar comment below.