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.