There is no reason that consecutive time units have unequal lengths. An hour is an hour. A week is a week.
52 weeks divide with 2, 4, 13 and 26.
Actually this Fixed fixed calendar does not need months at all. A year could just consist of 52 numbered weeks or 4 months of 13 weeks.
365 divides with 5, 73. These are not good candidates. 366 divides with 2, 3, 6, 61, 122, 183, 366 nothing too good here either. 364 divides with 2, 4, 7, 13, 14, 26, 28, 52, 91, 182. Now we have few choiches. 7 months would give 52 day months but 4 or 13 day weeks. 14 months give us 26 days in a month but two 13 day weeks. 26 months -> 14 days -> 2 weeks. 13 months -> 28 days -> 4 weeks.
7 day weeks have been proven practical.
We should standardize this so that week numbers are not ambiguous. There could be some superstition with fridays and 13 in every month so we better not start a week with Sunday.
Why shouldn't they? 30th december belonging to the next years first week is terrible practice. Week numbers in US and EU differ and this is wrong.
As 364 divides better than 365 we have this extra day. It is best to put this to the end of the year so we could number all days.
We could add this day to 7th month to distribute our extra days more evenly but this could be more confusing than 29th February. So again - it is best to put this to the end of the year so we could number all days.
That's the key point to keep everything aligned. These days should be for resting, celebrating and stock inventory. Stay home. Bank intrests are freezed.
Gregorian 1st January has nothing special to it. When we switch calendars we need to skip some 10 days from the last Gregorian year. This is nothing too unusual. We humans have done this multiple times.
If Jesus even existed he certainly was not born on year 1. Year 1 AD is not historicaly or cosmologically special.
Some countries have their own month names. Chinese have them just numbered.
Not too important. Let's just have 5 workdays and 2 days off.