The year was built around it, not the other way. It’s all derived from the Christian calendar. I’m not sure off the top of my head how Christmas ended up a few days before New Years, but they’re deliberately very close. It has been argued that the real life birth might not have been in winter at all (or even Bethlehem).

I digress, though. It would inevitably be lopsided somehow, because you’ve centered the numbering system around six months off of the New Years points.