First of all, of course there are always going to be seasonal differences and latitudinal variation for any of your given time zones. Alaska will experience the midnight sun etc.

What we have now is fairly kind to our natural "circadian" rhythms. The people on the eastern end of a large region will be going to work in the sun all happy while the people on the western end will be dragging themeselves to work in the dreary dark of night.
But I don't think that's what you are talking about is it?

You said nothing changes. Won't we always have to account for these differences no matter how we slice things up or how we number this sphere or follow time?