But what I was actually asking for was an example of a scenario where this wrapping gives us some benefit that we wouldn't have otherwise.

My original comment on that topic was:

Utility based models are most useful when applying general theorems - or comparing across architectures. For example when comparing the utility function of a human with that of a machine intelligence - or considering the "robustness" of the utility function to environmental perturbations.

Utility-based models are a general framework that can represent any computable intelligent agent. That is the benefit that you don't otherwise have. Utility-based models let you compare and contrast different agents - and different types of agent.