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Yes, you are right. However even a log utility function does not let you escape a Pascal mugging (you just need bigger numbers).
Risk aversion (in reality) does not boil down to a concave utility function. So the OP's claim that a well-defined utility function will fully determine the optimal risk-reward tradeoff is still false.
Why would maximizing expectation on a concave utility function lead to losing your shirt? It seems like any course of action that predictably leads to losing your shirt is self-evidently not maximizing expected concave-utility-function, unless it's a Pascal mugging type scenario. I don't think there are credible Pascal muggings in the world of personal finance, and if there are I'd be willing to accept an ad hoc axiom that we limit our theory to more conventional investments.
Now, I'll admit it's possible we should have a loss averse utility function, but we can do that without abandoning the mathematical approach--just add a time derivative of wealth, or something.