[FooBarBizBazz]

It would make sense to allow a risk-averse utility function in our framework (say a concave function of total dollars at the end).

I don't think the identification "volatility" = "standard deviation" = "risk" matches anyone's actual preferences. So that part doesn't make sense to me.

But I like your example with the medical treatment. That could be modeled with a step utility function. Mixing it with my example, there'd be no problem choosing my Asset 2 or 3, since both guarantee that your capital will be preserved so you can pay for your treatment. If your utility function were truly a step, you'd be indifferent between Assets 2 and 3. More realistically, you'd assign minus infinity to values beneath the threshold and some monotonic function to values above (e.g. just the number of dollars), and you'd prefer Asset 2: It guarantees your medical treatment, which is what you really care about, but it throws in a free lottery ticket, so why not take that.