Fax cover pages often act as ‘dividers' to piles of paper – electronic or hard copy. Many offices still receive faxes by hard copy – and this remains the default assumption as the ‘lowest common denominator'. I think that the dividers still serve a purpose.
Perhaps more importantly, there is a common practice that the cover page is the identifier of where the document originated, the intended purpose the information was provided, who the information is addressed, and who authorized the sending of the information.
Often the cover page provides clarity to the identify of the individual the information is about. Many healthcare providers use the cover page as their ‘disclosure log' to meet legislative compliance to clearly document disclosure of health information of a individual. I don't think it is feasible to add the information to the source document.
The receiver of the information needs this information in order to determine if they will accept the responsibility of collecting the information and the purpose for that information.
Perhaps the better approach is to make the cover page more useful – to both the receiving and sending party – by improving the documentation and adding suggested indexing categories. This can be easily generated if the sending party is using an EMR.
See also: Canadian EMR http://blog.canadianemr.ca/canadianemr/2013/11/a-complication-of-paper-faxes.html