the frequentist method says to use success/total

This is false (as explained in the linked-to video). If nothing else, the frequentist answer depends on the loss function (as does the Bayesian answer, although the posterior distribution is a way of summarising the answer simultaneously for all loss functions).

I think you're taking the frequentist interpretation of what a probability is and trying to forcibly extend it to the entire frequentist decision theory. As far as the "frequentist interpretation of probability" goes, I have never met a single statistician who even explicitly identified "probabilities as frequencies" as a possible belief to hold, much less claimed to hold it themselves. As far as I can tell, this whole "probabilities as frequencies" thing is unique to LessWrong.

Everyone I've ever met who identified as a frequentist meant "not strictly Bayesian". Whenever a method was identified as frequentist, it either meant "not strictly Bayesian" or else that it was adopting the decision theory described in Michael Jordan's lecture.

In fact, the frequentist approach (not as you've defined it, but as the term is actually used by statisticians) is used precisely because it works extremely well in certain circumstances (for instance, cross-validation). This is, I believe, what Mike is arguing for when he says that a mix of Bayesian and frequentist techniques is necessary.