Those divisions are already skewed in a 12 month calendar though because the number of days is not similarly divisible:
Half year (6 months)
1st half: 181 days (182 for leap years)
2nd half: 184 days
Quarter year (3 months)
1st quarter: 90 days (91 for leap years)
2nd quarter: 91 days
3rd quarter: 92 days
4th quarter: 92 days
A leap year has 366 days which is evenly divisible by 2 and yet even then a “half year” at the monthly level doesn’t contain half the days of the year. Having uneven yearly divisions in a 13 month calendar would not be a new problem.
You would then lose the ability to divide the year into pieces, since 13 is prime.
No half-yearly, quarterly or bi-monthly rhythm.
Our quarters don’t follow the actual half anyway, with the solstice and equinox not matching up with the months.
The divide is easy, and can be marked on the calendar like a holiday.
Much more convenient than making the whole calendar inconsistent.
Those divisions are already skewed in a 12 month calendar though because the number of days is not similarly divisible:
Half year (6 months)
1st half: 181 days (182 for leap years)
2nd half: 184 days
Quarter year (3 months)
1st quarter: 90 days (91 for leap years)
2nd quarter: 91 days
3rd quarter: 92 days
4th quarter: 92 days
A leap year has 366 days which is evenly divisible by 2 and yet even then a “half year” at the monthly level doesn’t contain half the days of the year. Having uneven yearly divisions in a 13 month calendar would not be a new problem.