In case all columns of a record have been set to null due to data type incompatibility, should we insert it at all?
Yes. In particular not all columns in the table need be specified in the copy command so while the parsed input data is all nulls the record itself may not be.
The system should allow the user to exclude rows with incomplete data by ignoring a not null constraint violation.
In short we shouldn't judge non-usefulness and instead give tools to the user to decide for themselves.
