@KristianHarstad No, Newtonian mechanics is clearly wrong, it does not fit experimental data. It's been proven wrong in multiple different ways.
It's what is generally taught to students first and it's what most engineers use to solve problems.
It is useful despite being wrong and not fitting experimental data.
I don't see any straw man argument, please refrain from this kind of accusations if you just didn't understand what I meant.

Utility is subjective indeed, and as such the utility of a theory is subjective. I'm not saying we should not investigate things that don't appear to be useful, just that the final objective of those investigations is making something useful.

Occam's razor only applies when choosing among different theories that fit all the data.
You can ignore data and small effects, it is regularly done in scientific investigation, methodologies and calculations.