Why doesn't the IUIE list valid 4-character BARR printer ID's?

No list of valid printers is available within the IUIE.

Because BARR is essentially a registration service for personally/departmentally owned printers, users are expected to know the BARR printer ID's that they need to use.

The Distributed Printing group maintains web pages that list BARR printers and the forms they support.

BARR Printer Support

Knowledge Base listing of BARR Printers and Forms

Distributed Printing

You can also contact your local computer support provider if you have any questions regarding the BARR printers ID's available to you.