Well the issue with 'utility maximization' is that people instantly think of some real valued number that is being calculated, compared, etc. That's not how it can possibly work in practice. In practice, you have unknowns; but you don't always need to assign defined numerical values to unknowns to compare expressions involving unknowns.

In the case of money, having more money results in no lower future utility than having less money, because in the future there's option to give up the money should they be found harmful - that's almost independent of how the utility function is defined.

Actually, think of chess as example. Final utility values are win, tie, and loss. A heuristic that all chess players use is to maximize the piece disbalance - have more pieces than opponent, better located perhaps, etc. - in the foreseeable future, if they can't foresee the end of game. This works for many games other than chess, which have different win conditions.