I believe this is also why we have 360 “degrees” in a circle, and not 365. The ancients hated that a year was clise to, but not exactly, 365 days. They chalked it up to the imperfection of Earth relative to the heavens. But a perfect year should be 360 days because it is divisible by every single digit number but 7.
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.