Is there a performance or storage space advantage to lowering time/timestamp precision in PostgreSQL?

PostgreSQL allows time/timestamp to specify a precision:

time, timestamp, and interval accept an optional precision value p which specifies the number of fractional digits retained in the seconds field. By default, there is no explicit bound on precision. The allowed range of p is from 0 to 6.

From PostgreSQL 13 Documentation

However it states that storage space is a constant 8-bytes for (timestamp and time without timezone) and 12-bytes for time with timezone regardless of p.

In the case that one doesn’t need extra precision — say milliseconds(p = 3) or seconds(p=0) would suffice — is there an advantage to explicitly lowering the precision?