If you are really paying attention, you may be a bit confused, because it seems to you that money or time or some other consumable resource can force you to assign utilities even if there is no uncertainty in the system. That issue is complex enough to deserve its own post, so I'd like to delay it for now.

It seems simple enough to me- when making decisions under certainty, you only need an acyclic preference ordering. The reals are ordered and acyclic, but they also have scale. You don't need that scale under certainty, but you need it to encode probabilistic preferences under uncertainty.