Web-to-Case and Email-to-case fields do not display on the Case detail page

The fields in question are standard fields that are unique to the Case object, and were designed with the intent that they would only be used by Web-to-Case, and Email-to-Case.  As a result, values can only be entered into these fields through one of the processes below:

• Web-to-Case
• Email-to-Case (client or on-demand)
• Integration that uses the API (if the fields in question have had the "read only" property removed via FLS and/or Page Layouts

If you create a Case record manually in the user interface these fields will not be accessible/editable, but will display if the fields are populated via web-to-case, email-to-case, or API.  Once these fields are populated, they are then editable in the UI, but if the field values are later removed via the user interface, the fields will disappear from the page layout again, and would only be accessible via the API afterwards.

Customers who cannot work with this behavior, should use custom fields on the case object to capture the desired information instead of these standard fields noted.

Note: This behavior is only applicable in Classic. Web-to-case fields are visible in Lightning Experience User Interface. 

Additional Information:
In Setup, the field API Names are displayed as below:

Web Company - SuppliedCompany
Web Phone - SuppliedPhone
Web Email - SuppliedEmail
Web Name - SuppliedName

See also:
Set Up Web-to-Case
Case Fields