If you return to a state you have already been at, you know you are going to be waiting forever and lose and get nothing.

You seem to be assuming here that returning to a state you have already been at is equivalent to looping your behavior, so that once a Turing machine re-enters a previously instantiated state it cannot exhibit any novel behavior. But this isn't true. A Turing machine can behave differently in the same state provided the input it reads off its tape is different. The behavior must loop only if the the combination of Turing machine state and tape configuration recurs. But this need never happen as long as the tape is infinite. If there were an infinite amount of stuff in the world, even a finite mind might be able to leverage it to, say, count to an arbitrarily high number.

Now you might object that it is not only minds that are finite, but also the world. There just isn't an infinite amount of stuff out there. But that same constraint also rules out the possibility of the utility box you describe. I don't see how one could squeeze arbitrarily large amounts of utility into some finite quantity of matter.