Sure, the problem is not which point on the ROC curve you pick, the problem is which classifier you use to obtain it in the first place. I can pick a random cla

Sure, the problem is not which point on the ROC curve you pick, the problem is which classifier you use to obtain it in the first place. I can pick a random classifier with a tunable parameter and draw its ROC curve and then pick the "optimal" point, but if the classifier sucks then that's no good. Why would a frequentist classifier based on a hypothesis test be good? A hypothesis test is the answer to the wrong question for the purposes of making a decision. As I showed above, you can indeed get the same result from Bayesian decision making if you use a weird prior and utility function, which shows that frequentist decision making based on hypothesis tests is a subset (of measure 0) of Bayesian decision making. Again, that just means that you encoded a most likely wrong prior and utility in the choice of method without any justification.