"Utility" can be a scientific concept, or it can be a just-so word.
a) propose a hypothesis, a mathematical theory (or model) of some physical process, e.g. of people making choices.
b) find a testable prediction.
c) check that prediction against observation.
Utility theory makes the following kind of prediction.
1) Observe someone's behavior, and infer u(x).
2) use u(x) to predict future behavior.
But if u(x) is allowed to change, then no prediction is possible, science can't operate, and utility becomes a non-scientific concept.
"Paul did X"
"Paul had utility to do X."
With changing u(x) the latter is unnecessarily complicated and scientifically equivalent.