Should the time zone be recorded in case of time or not?

WITH temporal_column AS (SELECT table_schema, table_name, column_name, data_type, ordinal_position
FROM INFORMATION_SCHEMA.columns
WHERE data_type IN ('time without time zone', 'time with time zone')
AND (table_schema, table_name) IN (SELECT table_schema, table_name
FROM INFORMATION_SCHEMA.tables WHERE table_type='BASE TABLE') AND 
table_schema NOT IN (SELECT schema_name
FROM INFORMATION_SCHEMA.schemata
WHERE schema_name<>'public' AND
schema_owner='postgres' AND schema_name IS NOT NULL))
SELECT table_schema, table_name, column_name, data_type
FROM Temporal_column
WHERE EXISTS (SELECT 1 FROM Temporal_column WHERE data_type='time without time zone')
AND EXISTS (SELECT 1 FROM Temporal_column WHERE data_type='time with time zone')
ORDER BY data_type, table_schema, table_name, ordinal_position;