That is expected and documented behaviour:
From the manual:
Since these functions return the start time of the current transaction, their values do not change during the transaction. This is considered a feature: the intent is to allow a single transaction to have a consistent notion of the “current” time, so that multiple modifications within the same transaction bear the same time stamp.
If you want something that changes each time you run a statement, you need to use statement_timestamp() or even clock_timestamp() (again see the description in the manual)