no, the one where there are years without a january 1, and years with two january 1. there's nothing that says january 1 has to be new years, and in some cultures it already isn't. there's also nothing that says you can't continue celebrating january 1 as the new year, while using a week-day calendar for all official purposes.

a new calendar not mapping cleanly to the current months hardly seems like a valid criticism of a calendar that intentionally doesn't map to the current months.