If the day that we now call Dec. 21 would be picked as the start of a new year, it would at least have the significance of starting at some logical point in the earth's orbit. Being a few hours off is better than being 10 days off. The year wouldn't vary in length anymore than it does now - 365.25 days. It just would start being called "new year" 10 days sooner. Leap year would still be needed of course, just like we need it now.
If the calendar could be changed in other times through out history, why not again?