The question is, given it isn't always applicable, and it may not always be necessary where it is partially so, are there situations where it causes paradoxes where it is a source of noise instead of information, and how can we know when applying it whether it causes one or the other?
Godel as a logician would have approached it as just another formalism.
If reconciling models of physical phenomena with models of time produces inconsistency and paradoxes, he'd ask whether we were first sure that was time intrinsic to those physical phenomena, or does our model of time impose an arbitrary constraint on our ability to reason more abstractly about them.
My point is that it's a reasonable question with related applications. Not sure there is a wrong to be here.