[tlb]

It's appropriate when the cost of false-positive and false-negative errors are the same. Which isn't common in the real world.

[kqr]

More generally, if one views probability as separate from the utility of the outcome it's attached to, one is bound to make bad decisions.

Real decision problems contain a lot of nonlinearities if decomposed the wrong way. The only way to decompose it is as a linear combination of probability and utility (because the utility swallows the nonlinearities). But for each component both probability and utility matters in determining the overall value of the decision.