Yes! Thank you for saying this clearly and distinctly.

Real-world objects are never perfect spheres or other mathematical entities. However, math is quite useful for modeling them. But the way we decide which math is the right math to use to model a particular sort of object is through repeated experiment. And sometimes the trajectory through spacetime of a given object (say, a gold coin of a certain mass) is best modeled by certain math (e.g. ballistics) and sometimes by other very different math (e.g. economics).

Utility functions belong to the math, not the territory.