Pandas Calling pd.PeriodIndex constructor on pd.Index cannot infer frequency, while first calling pd.DateTimeIndex on pd.Index and calling .to_period() does work

I have the following pd.Index: Index(['2021-01-01', '2021-02-01', '2021-03-01', '2021-04-01', '2021-05-01', '2021-06-01', '2021-07-01', '2021-08-01', '2021-09-01', '2021-10-01', '2021-11-01', '2021-12-01', '2022-01-01', '2022-02-01', '2022-03-01', '2022-04-01', '2022-05-01', '2022-06-01', '2022-07-01', '2022-08-01', '2022-09-01', '2022-10-01', '2022-11-01', '2022-12-01'], dtype='object', name='period')

I want to transform this index to a pd.PeriodIndex. I tried this using the pd.PeriodIndex constructor, but this give the following error: {ValueError}freq not specified and cannot be inferred.

However, if I first call pd.DateTimeIndex on the index and then call the .to_period() method on the resulting DateTimeIndex, the result is as expected: PeriodIndex(['2021-01', '2021-02', '2021-03', '2021-04', '2021-05', '2021-06', '2021-07', '2021-08', '2021-09', '2021-10', '2021-11', '2021-12', '2022-01', '2022-02', '2022-03', '2022-04', '2022-05', '2022-06', '2022-07', '2022-08', '2022-09', '2022-10', '2022-11', '2022-12'], dtype='period[M]', name='period').

This does not make sense to me: apparently the frequency CAN be inferred form the original index, but the pd.PeriodIndex constructor is not equipped for this.

Comment From: jbrockmendel

freq means something different for DatetimeIndex than it does for PeriodIndex. It's unfortunate but hard to change at this point. The freq that cannot be inferred when you call PeriodIndex on your strings refers to the resolution of each entry. DatetimeIndex.to_period using self.inferred_freq which refers to the spacing between entries.