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"