You don't imagine that when someone, say, characterizes a financial asset as having the expected return of 5% with 20% volatility, these probabilities are precise, do you?

Those are not even probabilities at all.

There are two very different sorts of scenarios with something like "imprecise probabilities".

The first sort of case involves uncertainty about a probability-like parameter of a physical system such as a biased coin. In a sense, you're uncertain about "the probability that the coin will come up heads" because you have uncertainty about the bias parameter. But when you consider your subjective credence about the event "the next toss will come up heads", and integrate the conditional probabilities over the range of parameter values, what you end up with is a constant. No uncertainty.

In the second sort of case, your very subjective credences are uncertain. On the usual definition of subjective probabilities in terms of betting odds this is nonsense, but maybe it makes some sense for boundedly introspective humans. Approximately none of the decision theory corpus applies to this case, because it all assumes that credences and expected values are constants known to the agent. Some decision rules for imprecise credence have been proposed, but my understanding is that they're all problematic (this paper surveys some of the problems). So decision theory with imprecise credence is currently unsolved.

Examples of the first sort are what gives talk about "uncertain probabilities" its air of reasonableness, but only the second case might justify deviations from expected utility maximization. I shall have to write a post about the distinction.