38175 added correct handling of nanoseconds in the Period constructor but the code path as is parses the input twice. We should integrate the nanoseconds code into parse_time_string so this happens only once.

xref https://github.com/pandas-dev/pandas/pull/38175/files#r536100941

It might be worth adding a nanosecond Period constructor benchmark too.

Comment From: jorisvandenbossche

BTW, the reason I noted this is actually already thanks to our benchmarks: https://pandas.pydata.org/speed/pandas/#period.PeriodIndexConstructor.time_from_ints?python=3.8&Cython=0.29.21&p-freq='D'&p-is_offset=False&commits=02caf7d7-daa59420