In practice, guessing at numbers and running a calculation actually serves as a quick second opinion on your original intuitive decision. If the numbers imply something far different from the decision that System 1 is offering, I don't immediately shrug and go with the numbers: I notice that I am confused, and flag this as something where I need to consider the reliability both of the calculation and of my basic intuition. If the calculation checks out with my original intuition, then I simply go for it.

Basically, a heuristic utility calculation is a cheap error flag which pops up more often when my intuitions are out of step with reality than when they're in step with reality. That makes it incredibly valuable.