But 13 months of 28 days is only 364 days. After 28 years, the months would be shifted and the seasons would no longer line up, which throws off a whole lot of stuff that needs proper timing like farming. It's not perfect, but the current calender is the way it is for a reason.
I really like it because in order to keep the days of the week aligning that holiday must be a special non day of the week. It would lead to conversations like. "What day of the week is it?" "It isn't"
I would prefer 12 months of 30 days each, 6 days per week, then an intercalary week of 5-6 days. 6 days per week means 4 day work week, staggered weekends for those jobs where 24/6 availability would be preferred.
As long as we're wishing for things, I also would like to change our base 10 system for a base 12 system (duodecimal or dozenal). 12 is a superior highly composite number, and it's a bit easier to divide things into thirds, which is more common than fifths.
Seems weird since one of the 12 betrayed him, and maybe a thirteenth disciple would have exposed the plot and Jesus would have avoided crucifixion, thus sparing the world centuries of oppression and war.
My fundamentalist dad told me it was because the first passover (when God killed the first born son of every Egyptian household that didn't have lamb's blood) landed on Friday the 13th. Take that with a grain of salt.