What you want to "put in your utility function" is... the effect of choices on your ability to estimate and optimize your utility function. That's making the utility function recursive, building a "strange loop to the meta level" between your utility and the optimization algorithm which is supposed to maximize the utility function. And I don't see any reason (but maybe there are) why that recursion should converge and be computable in finite time.

But (essentially to repeat a point) it would be a bias, since the adjustment is based on risk, whereas it should ('assuming everything else) be based on uncertainty (risk multiplied by the length of time the result is unknown). But even if the adjustment were based on the relevant factor, it would still be a bias because the adjustment should concern not only the time but on the chances that relevant decisions will be required in the interval.

A separate point—One topic that should be considered in evaluating the argument further is whether other decision problems introduce the same "strange loops."

Utility function is supposed to contain only terminal values. You're not supposed to factor instrumental values into your utility function.

Utility functions are typically defined over expected futures. A feature of that future is how many seconds and calories you spent making decisions (and thus not doing other things). And so if a gamble will give you either zero or a hundred calories, but take fifty calories to recompute all of your plans that depend on whether or not you win the gamble, then it's actually a gamble between -50 and 50 calories, not 0 and 100.

In short, utility functions should take terminal values as inputs, but those terminal values depend on instrumental values, and your utility function should respond to that dependence.