On the matter of days in a years, there's also the idea of spliting the year into 13 months of 28 days each for a total of 364 days, closer matching the lunar cycle (and women's body). Every day of the year would always be on the same day of the week.

Then the extra day? It's world day, a global holiday for celebrating the new year, and it doesn't belong in any weekday. Sometimes we'd need an extra leap year day (just like right now with 29th February) so they would just both be world day.

https://en.m.wikipedia.org/wiki/International_Fixed_Calendar

Check for pros and cons.