The problem is that the utility isn’t constant. If you, today are indifferent to what happens on future Tuesdays, then you will also think it’s a bad thing that your future self cares what happens on that Tuesday. You will therefore replace your current self with a different self that is indifferent to all future Tuesdays, including the ones that it’s in, thus preserving the goal that you have today.
Good point. I have to remember not to confuse expected utility with future utility.